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UNIVERSITY OF LJUBLJANA
INSTITUTE OF MATHEMATICS, PHYSICS AND MECHANICS
DEPARTMENT OF THEORETICAL COMPUTER SCIENCE
JADRANSKA 19, 1 000 LJUBLJANA, SLOVENIA
Preprint series, Vol. 40 (2002), 568/2
LAYOUTS FORGRAPH DRAWING CONTESTS
1995-2001
Vladimir Batagelj, Andrej Mrvar
ISSN 1318-4865
Version 1: May 13, 1998Version 2: December 27, 2001
Math.Subj.Class.(2000): 05 C 90, 68 R 10, 76 M 27, 68 U 05,05 C 50, 05 C 85, 90 C 27, 92 H 30, 92 G 30, 93 A 15, 62 H 30.
Supported by the Ministry of Education, Science and Sport of Slovenia,Project J1-8532.
Address: Vladimir Batagelj, University of Ljubljana, FMF, Departmentof Mathematics, and IMFM Ljubljana, Department of TCS, Jadranskaulica 19, 1 000 Ljubljana, Slovenia
e-mail: [email protected]
Ljubljana, December 27, 2001
Layouts forGraph Drawing Contests
1995-2001
Vladimir BatageljDepartment of Mathematics, University of Ljubljana
Andrej MrvarFaculty of Social Sciences, University of Ljubljana
Graph drawing contests
Since 1994 graph drawing contests are organized as a part of the Graph Drawing Confer-ences. The rules and data are described on Internet and participants send their drawingstill the specified date. They can use any technique to get layouts of graphs. The primaryjudging criterion is how well the drawings convey the information in the graphs: vertexidentifiers, vertex types, and vertex interconnectivity. A secondary criterion is the degreeto which manual editing was employed to produce the layout: the less manual intervention,the better.
The purpose of the contests is to monitor and challenge the current state of the art ingraph-drawing technology.
Data (vertices and lines) for 3 or 4 graphs are given each year. A winning entry for eachgraph is chosen by a panel of experts.
In this paper we collected our submissions to the contests in the years 1995–2001. Theyare available also at
http://vlado.fmf.uni-lj.si/pub/gd/gd95.htmand the original data (and their versions in Pajek format) at
http://vlado.fmf.uni-lj.si/pub/networks/data/gd/gd.htmThere you will find also pictures in some (dynamical) graphical formats (VRML, SVG) thatcan not be adequately reproduced in the paper form.
2
Layouts for Graph Drawing Contest 1995
In 1995 the Graph Drawing Conference was helt in Passau and the contest was organizedby Peter Eades and Joe Marks. Rules and data are described at:
http://www.uni-passau.de/agenda/gd95/contest.html
Graph A95� First layout was obtained automatically using our program COORD (positioning ver-tices on the rectangular net so that the number of crossings of lines is as low aspossible).
� Manual editing was performed to reposition vertices using our graph picture editorDRAW.
Graph B95� Analysing graph B using our program RELCALC two central vertices were found (1and 34).
� Feasible possitions for vertices were generated (two families of concentric circles).
� Vertices 1 and 34 were fixed in the centre of the concentric circles mentioned.
� Other vertices were automatically positioned around using program COORD so thatthe total length of the lines was minimized.
� Layout was then edited manually using DRAW to reposition vertices to minimizecrossings (concentric circles cannot be seen any more).
The layout was awarded the honorable mention.
Graph C95� First layout was obtained automatically using our program ENERG (minimisation ofENERGy).
� Some manual editing using DRAW was performed to reposition vertices.
The layout was awarded the first prize.
See: http://vlado.fmf.uni-lj.si/pub/gd/gd95.htmThe complete report of the contest is available in [6] and:
http://www.merl.com/reports/TR95-14/index.html
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Figure 1: Graph A95.
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MUX1
INSTRUCTION BUFFER (4 x 16)2
RCV3
DRV4
ROM REG5
MUX6
ROM ADDR7
MACRO INSTRUCTION ROM8
MUX9
L210
MUX11
GENERAL REGISTER FILE (32 x 32)12
ALU13
A STAGE14
MUX15
L116
MUX17
SHIFTER18
MUX19
J REG20
PROGRAM COUNTER21
PSW SSW22
B STAGE23
C STAGE24
PIPELINE CONTROL25
OUTPUT26
ALIGN27
INPUT28
MUX29
R30
ALU31
ACCUMULATOR32
FPU REGISTER FILE (8 X 64)33
ENCODER34
INSTRUCTION BUS TO I-CAMMU35
DATA BUS TO D-CAMMU36
INSTRUCTION BUS INTERFACE
MACRO INSTRUCTION UNIT
INTEGER EXECUTION UNIT
INSTRUCTION CONTROL UNIT
DATA BUS INTERFACE
FLOATING POINT UNIT
EXTERNAL
Figure 2: Graph A95 descriptions.
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Figure 3: Graph B95 (honorable mention).
6
graphics.c:GRDisplayPoint1
long1.c:GRDisplayPoint2
long2.c:GRDisplayPoint3
short.c:GRDisplayPoint4
X11/X.h:GCFont5
gremlin.h:dby_to_win6
X11/X.h:GXxor7
X11/X.h:GCFunction8
X11/Xlib.h:XGCValues9
gremlin.h:dbx_to_win10
graphics.c:text_pf11
main.c:pix_gc12
main.c:display13
X11/Xlib.h:XChangeGC14
X11/Xlib.h:XCopyPlane15
/usr/include/strings.h:strlen16
main.c:Artmode17
main.c:SUN_YORIGIN18
main.c:SUN_XORIGIN19
main.c:pix_sw20
X11/Xlib.h:XDrawString21
/usr/include/stdio.h:sprintf22
icons/icon.littlepoint:littlepoint_pm23
X11/Xlib.h:struct Xlib_h_324
X11/Xlib.h:XFontStruct25
icondata.c:mpr_static26
gremlin.h:PMRec27
X11/Xlib.h:Display28
gremlin.h:FALSE29
X11/X.h:Window30
X11/Xlib.h:GC31
gremlin.h:struct PMRec32
X11/X.h:Font33
X11/Xlib.h:struct _XDisplay34
X11/Xlib.h:Bool35
X11/Xlib.h:struct _XGC36
X11/X.h:Pixmap37
X11/X.h:XID38
X11/Xlib.h:struct Xlib_h_5739
X11/Xlib.h:ScreenFormat40
X11/Xlib.h:struct Xlib_h_2241
X11/Xlib.h:Status42
X11/Xlib.h:struct Xlib_h_2143
X11/Xlib.h:XCharStruct44
X11/Xlib.h:XExtData45
X11/X.h:KeySym46
X11/X.h:GContext47
X11/Xlib.h:Screen48
X11/Xlib.h:XModifierKeymap49
X11/Xlib.h:XFontProp50
<void>:struct _XrmHashBucketRec51
<void>:struct _XKeytrans52
<void>:struct _XIMFilter53
<void>:struct _XExten54
<void>:struct _XContextDB55
<void>:struct _XFreeFuncs56
<void>:struct _XSQEvent57
<void>:struct _XDisplayAtoms58
X11/Xlib.h:struct Xlib_h_2059
X11/Xlib.h:struct Xlib_h_760
X11/Xlib.h:struct _XExtData61
X11/Xlib.h:XPointer62
X11/Xlib.h:struct Xlib_h_663
X11/Xlib.h:struct Xlib_h_5664
X11/Xlib.h:struct Xlib_h_5565
X11/X.h:Atom66
X11/Xlib.h:Depth67
X11/X.h:Colormap68
X11/X.h:KeyCode69
X11/Xlib.h:Visual70
X11/Xlib.h:struct Xlib_h_571
X11/Xlib.h:struct Xlib_h_472
X11/X.h:VisualID73
procedure
macro
type
variable
Figure 4: Graph B95 descriptions.
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Figure 5: Graph C95 (first prize).
8
t11
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t66
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t-node
o-node
Figure 6: Graph C95 descriptions.
9
Layouts for Graph Drawing Contest 1996
In 1996 Graph Drawing Conference was helt in Berkeley, and the contest was organized byPeter Eades, Joe Marks, and Stephen North. Rules and data are desribed at:
http://portal.research.bell-labs.com/orgs/ssr/people/north/contest.html
Graph B96� First layout was obtained automatically using our program COORD. (positioning ver-tices on the rectangular net so that the number of crossings of lines is as low aspossible).
� Manual editing was performed to reposition vertices using our graph picture editorDRAW.
The layout was awarded the honorable mention.
Graph C96� Analysing graph C using our program RELCALC two parts and 2 connecting verticeswere found.
� Each part was handled separately using our program ENERG (minimisation of en-ergy). One part consists of a lattice structure, and the second of a planar graph ofcylindric symmetries. This spatial picture was realized in VRML (produced from thedescription in our graph description language NetML based on SGML).� Some manual editing was done for planar representation.
The layout was awarded the first prize.
Graph D96� Analysing graph D using program RELCALC 17 important vertices of ’kernel graph’were found.
� The first layout for these 17 vertices was obtained automatically using program COORD.� Other vertices were added to the obtained picture.
� Some manual editing using DRAWwas performed to reposition vertices to avoid cross-ings.
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Figure 7: Graph B96 (honorable mention).
See: http://vlado.fmf.uni-lj.si/pub/gd/gd96.htmThe complete report of the contest is available in [10] and:
http://www.merl.com/reports/TR96-24/index.html
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207-555
415-555
303-555
617-555
313-555
406-555
304-555
603-555
Figure 8: Graph B96 types.
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207-555-82481
415-555-21882
415-555-60333
303-555-43934
617-555-97655
313-555-03296
415-555-79627
313-555-85638
207-555-18039
406-555-083610
303-555-795511
617-555-926012
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415-555-826732
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415-555-333035
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303-555-454338
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603-555-432161
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603-555-656568
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304-555-516770
415-555-590871
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617-555-920673
303-555-922374
415-555-760275
415-555-119776
304-555-466077
207-555-167678
406-555-128579
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303-555-648182
617-555-625783
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415-555-881285
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603-555-121392
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415-555-835597
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617-555-1958100
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313-555-4790105
313-555-7556106
603-555-0525107
406-555-5703108
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415-555-6423110
603-555-5694111
Figure 9: Graph B96 labels.
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Figure10:G
raphC
96(firstprize).
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Figure 11: Graph C96 / VRML snapshot.
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Figure 12: Graph C96 with cylinder / VRML snapshot.
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Figure 13: Graph D96.
17
For Your Business1
http://www.att.com/work/2
Employment3
http://www.att.com/hr/4
800 number5
http://www.tollfree.att.net/dir800/6
News for the Month7
http://www.att.com/news/8
AT&T Corporate Server Team9
http://www.att.com/homes/10
Library11
http://www.att.com/library/12
On The Net13
http://www.att.com/net/14
Lucent Technologies15
http://www.att.com/lucent16
Copyright17
http://www.att.com/copyright.html18
AT&T Home Page19
http://www.att.com/20
Site Map21
http://www.att.com/sitemap22
Conferences23
http://www.att.com/news/conferences.html24
Work25
label026
Globe27
http://www.att.com/providers28
mailto:[email protected]
On The Net31
For Your Business32
Speeches Online33
http://www.att.com/news/speeches34
label035
http://www.att.com/hr/employment/overvie36
label137
http://www.att.com/hr/employment/matrix.38
label239
http://www.att.com/hr/employment/prof_de40
label341
http://www.att.com/hr/employment/support42
AT&T EasyLink Services (SM)44
http://www.att.com/easycommerce/easylink45
For Your Business46
Net47
AT&T/A-Z48
http://www.att.com/atoz49
For Your Home50
http://www.att.com/home51
CNI to offer AT&T and Unisource voice an52
http://www.att.com/press/0396/960313.bsa53
Site Map54
AT&T Easy World Wide Web (SM)55
http://www.att.com/easycommerce/easywww56
Search57
http://www.att.com/news/../search.html58
mailto:[email protected]
Write To Us61
http://www.att.com/write/62
Home Solutions63
http://www.att.com/home/homesol.html64
Copyright65
New U transceiver chips enable lower cos66
http://www.att.com/press/0396/960312.mea67
AT&T Global Alliance Marketing68
http://www.att.com/easycommerce/alliance69
For Your home70
InfoCenter71
http://www.att.com/infocenter72
Surfing for Savings?73
http://www.att.com/indiahorizons/connect74
On The Go75
http://www.att.com/onthego/76
Now shipping: Windows NT developer’s kit77
http://www.att.com/press/0396/960312.gba78
Business Network79
http://www.att.com/bnet/80
AT&T Home Page81
AT&T Universal Card82
http://www.att.com/ucs/83
AT&T/A-Z85
Search86
http://www.att.com/search.html87
TrueVoice88
http://www.att.com/true/truevoice.html89
On The Go90
Home Page91
http://www.att.com/index.html92
Thanks to the new telecommunications law93
http://www.att.com/press/0296/960208.cha94
Write To Us95
http://www.att.com/news/../write.html96
Search97
http://www.att.com/search/98
Copyright99
AT&T Corporate Server Team100
Search102
What’s New!103
http://www.att.com/whatsnew.html104
Site Map105
http://www.att.com/news/../sitemap.html106
Index107
http://www.att.com/infocenter/attindex.h108
You Will109
http://www.att.com/youwill/110
Write To Us111
Copyright112
AT&T WorldNet Service officially availab113
http://www.att.com/press/0396/960314.bsa114
Calendar115
http://www.att.com/easycommerce/easycomc116
Home117
On The Net118
On The Go119
For Your Home120
calling plan121
http://www.att.com/true/truefacts.html122
Copyright123
AT&T/A-Z124
http://www.att.com/news/../atoz.html125
Sonet T155 service gets first add/drop m127
http://www.att.com/press/0396/960313.bsb128
http://www.att.com/indiahorizons/129
http://www.att.com/indiahorizons/images/130
http://www.att.com/indiahorizons/images/131
http://www.att.com/images/hpbut28.gif132
http://www.att.com/net/yougotit.html133
http://www.att.com/images/lp72vcv.gif134
http://www.att.com/net/yougotit.html/ima135
http://www.att.com/easycommerce/images/t136
http://www.att.com/easycommerce/document137
http://www.att.com/images/hpbut06.gif138
http://www.att.com/easycommerce/139
http://www.att.com/images/bar.gif140
http://www.att.com/maps/bar.map141
http://www.att.com/easycommerce/images/h142
http://www.att.com/easycommerce/home.map143
http://www.att.com/easycommerce/images/m144
http://www.att.com/easycommerce/images/w145
http://www.att.com/images/ltbar2.gif146
http://www.att.com/images/attlogo-8hw.gi147
http://www.att.com/news/../images/topnav148
http://www.att.com/maps/topnav.map149
http://www.att.com/news/images/newshead.150
http://www.att.com/news/images/newsside.151
http://www.att.com/news/images/newssub.g152
http://www.att.com/news/images/newsheads153
http://www.att.com/news/newsside.map154
http://www.att.com/images/hpbut20.gif155
http://www.mckinley.com/156
http://www.att.com/hr/employment/images/157
http://www.att.com/hr/employment/nav.map158
http://www.att.com/images/index.gif159
http://www.att.com/images/hpbut19.gif160
http://www.att.com/hr/employment/images/161
AT&T - Employment Opportunities162
http://www.att.com/images/homesolu.gif163
http://www.att.com/images/athome.gif164
http://www.att.com/images/youwill2.gif165
http://www.att.com/images/truvoice.gif166
AT&T EasyCommerce Services167
http://www.att.com/maps/index.map168
http://www.att.com/infocenter/toc.html169
http://www.att.com/microscapes/microscap170
http://www.att.com/indiahorizons/home.ht171
http://www.att.com/easycommerce/whatsnew172
AT&T Home Page173
AT&T Newsroom174
http://www.att.com/maps/bar2.map175
AT&T at Home176
You Got It.177
http://www.att.com/hr/employment/images/178
AT&T India Horizons179
http://www.att.com/press/180
Figure 14: Graph D96 labels.
18
Layouts for Graph Drawing Contest 1997
In 1997 Graph Drawing Conference was helt in Rome and the contest was organised byPeter Eades, Joe Marks, and Stephen North. Rules and data are described at:http://portal.research.bell-labs.com/orgs/ssr/people/
north/contest.html
Graph A97� First layout was obtained automatically using draw/eigenvalues option in pro-gram Pajek. Manual editing was used to reposition vertices in the grid to obtainorthogonal layout in plane.
The layout was awarded the first prize.
� Manual editing in 3D was performed to get orthogonal embeddings in space: mini-mal, symmetric and cube.
Graph B97� Analysing graph B using our program MODEL we obtained (almost) regular partitionin 3 classes. The third class contains only vertex Harmony Central. The secondclass, represented by squares, contains 11 vertices that are connected only to thevertices in the class 1 (represented by circles). Vertices in class 1 are also connectedto other vertices in the same class. We first drew all vertices in the class 1 in the centerand vertices in class 2 separately – using class shrinking and circular drawing optionsin Pajek. Afterward we manually moved vertices of class 1 connected to only onevertex of class 2 close to this vertex. Finally we manually arranged the remainingvertices of class 1.
� We transformed given similarities � on arcs to dissimilarities��� ����� and applied
Ward’s hierarchical clustering method to the obtained dissimilarity matrix. We pro-duced a clustering into 12 clusters, shrank the graph using Pajek, and draw the ob-tained skeleton minimizing the number of crossings. Finally we manually arrangedthe vertices of original graph.
The layout was awarded the first prize.
See alsohttp://vlado.fmf.uni-lj.si/pub/gd/gd97.htm
The complete report is available in [7] or athttp://www.merl.com/reports/TR97-16/index.html
19
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Figure 15: Graph A97 – orthogonal layout in plane (first prize).
20
Figure 16: Graph A97 – 3D minimal / VRML snapshot.
21
Figure 17: Graph A97 – 3D symmetric / VRML snapshot.
22
Figure 18: Graph A97 – 3D cube / VRML snapshot.
23
1997 North American Gs Develop
Edirol Online
Virtual Sound Canvas Online
Microsoft Corporation Home Pag
Microsoft Netshow Events Calen
Wavelet Netcare
Wavelab
Wavelet Resources
IBM Corporation
Kasparov Vs. DeepBlue: The Rem
Guest Essay: David Stork
Boston At Night: Feature Story
Intranet Executive: Digital Id
Netscape Navigator Family
Netscape Devedge: Library
Netscape Devedge: Library 1
Netscape Devedge: Courses & Co
Netscape Devedge: Courses & Co
Four Corners Hantavirus
Bunyaviridae
INI International: Grocery Sec
INI International: Vitamins
INI International: Candy Secti
Journal EntryCelery
Onions
The Biting Truth
Musky Have Teeth
404 Not Found
Cold Front Tactics
Identifying Vegetation
Tackle Box Survival - Surface
Sandell & Associates Surface L
Musky Muskie Lure Components
Young Designer Of The Month
The London College Of Fashion
Designercity
Designercity1
Designercity2
Designercity3
Designercity4
Designercity5
Designercity6
Nada138-954
Janet’s Horsin’ Around On The
Equinet(tm) - Comments
Harmony Central: Midi Tools
Figure 19: Graph B97 – regular equivalence.
24
��� ������������������ �!� "$#%�!&'�)( �+*-,+./&).10324245687:9-;'<>=@?�6BADCFEHGIKJ�LNMPO J:Q RIKJ�LNMPO MTSTU$MTV WIKJ�LNMPO MTSTXYMZS [\Y]_^a`bJ�L_c dec f gNhikjHMTVTc lm^bMNdon pNq\3c SZc ^blsr3dt]bS gNRnu]�VavZ`Pr$MaMTSZw gNW\1xPVySzxm^N{|X)c S }ag~ ^_^bMTSTj|c l�~ f }ap� x�O f���d�x�^bSzr pNhXYJPf:J�}apsWN�sqb� �N�����]_c ^bMTS�rkn �_[� � x_dt^PMPd�V���L }a�� � n�c fmc r$x:xmO �_R� MNO MNd ` gNq� ^_c xm^�V gN[�bx�]_d!^PJ:O ��^bS gb�~ fN�HMTlsMTSyJbSZ^ p�}r1JP�PvNO Ms\1xa�N� pNg��J:^bf_MNO O ���HV pNp~�X�~ �)dFx:�aMPd�` g�}~�X�~ �'c SyJ:�+c ^ gNg~�X�~ � J:^bfs`N��� gNp�4c d��mx�]:^bf �-� pj)J�L:c f���Szx_dtv }N}�3JbVa�PJNd�xPLmj4\ }ahn%�1X3MTSoVawPxT� � q�:�3x_d�VTc ^_� �|d �_q�Pxm^bf:x�^:�sJ�Vaw pN[}a�s�NRmX3�'�+�-V�j }��fmc d�xmO � ^�� gn%�1�3xm��MN��JblsM �~�\Hn � xsdt�_xsd�J �XY��XYJ�L_c l:J�SZd }Z�nu]�VavZ`mn��:]_dFM pb�XY��jHMZL � x_� � x�}aW�_hP��X3ST�Pxm]_^Pf gN�XY��jHMZL��:c QNd ` }aqXY��jHMZL��:c QNd!} }a[XY��jHMZL � x_� � x�}aRjHMTVTc lm^P�Pc S q �_gjHMTVTc lm^P�Pc S [ �_pjHMTVTc lm^P�Pc S g pN�jHMTVTc lm^P�Pc Sa} pNWjHMTVTc lm^P�Pc Se` pNRjHMTVTc lm^P�Pc Sz� ��}jHMTVTc lm^P�Pc S p �_h
Figure 20: Graph B97 – Dendrogram for Ward’s method.
25
1997 North American Gs Develop
Edirol Online
Virtual Sound Canvas
Microsoft Corporation Home Pag
Microsoft Netshow Events Calen
Wavelet NetcareWavelab
Wavelet Resources
IBM Corporation
Kasparov Vs. DeepBlueGuest Essay: D. Stork
Boston At Night: Feature StoryIntranet Executive: Digital Id
Netscape Navigator Family
Netscape Devedge: Library
Netscape Devedge: Library 1Netscape Devedge: Courses & Co
Netscape Devedge: Courses & Co
Four Corners Hantavirus
Bunyaviridae
INI International: Grocery Sec
INI International: VitaminsINI International: Candy Secti
Journal EntryCeleryOnions
The Biting Truth
Musky Have Teeth
404 Not Found
Cold Front Tactics
Identifying Vegetation
Tackle Box Survival - Surface Sandell & Associates Surface L
Musky Muskie Lure Components
Young Designer Of The Month
The London College Of Fashion
Designercity
Designercity1Designercity2
Designercity3Designercity4
Designercity5Designercity6
Nada138-954
Janet’s Horsin’ Around On The
Equinet(tm) - Comments
Harmony Central: Midi Tools
Figure 21: Graph B97 – Ward’s clustering (first prize).
26
Layouts for Graph Drawing Contest 1998
In 1998 Graph Drawing Conference was helt in Montreal and the contest was organised byPeter Eades, Joe Marks, Petra Mutzel, and Stephen North. Rules and data are described at:
http://gd98.cs.mcgill.ca/contest/All work was done using our program package Pajek, which is freely available at:
http://vlado.fmf.uni-lj.si/pub/networks/pajek/
Graph A98
The data for graph A consist of addition and deletion operations that specify how the graphchanges over time. In our solution addition and deletion operations were performed us-ing macro language which is recognized by program package Pajek. Then we usedMicrosoft Camcorder (free software) to record the process. Selected layouts in threedifferent time points are shown.
Graph B98
Symmetries in graph (with some exceptions) can easily be noticed. We started the draw-ing using the layout obtained using Fruchterman-Reingold spring embedder. Later we usedmanual editing to maximize symmetries and made some displacements according to differ-ent sizes and shapes of nodes. Pajek was used to do all the work.
The layout was awarded the first prize.
Graph C98
Using spring embedders we could not get any nice layouts. Analysing graph we found thatit is a symmetric cubic graph. Later we used eigenvectors approach and computed eigenvec-tors of neighbourhood matrix that correspond to the largest eigenvalue (which is multiple).In this way we got nice symmetric picture in space (3D). According to symmetries (equiva-lences) some of the nodes are drawn on the same positions and some are overlapping whenselecting the certain view to see the symmetries. Since some vertices are overlapping webuilt a list of overlapping vertices drawn in different colors:
Graph D98
There were no data available for this graph. The participants could send any picture thatis inspired or related to graph drawing. We decided to generate graph from dictionary andsent some interesting subgraph of it.
27
Table 1: Overlapping vertices in graph C98
Group Color Vertices1. Yellow 13, 762. Green 9, 12, 33,1063. Pink 39, 65, 88,1124. Blue 5, 20, 51, 635. Fuchsia 68, 75, 85, 926. White 36, 997. Orange 21, 428. Purple 23, 24, 55, 899. NavyBlue 30, 44, 54, 57
10. TealBlue 3, 11, 43,10111. OliveGreen 1, 18, 64, 74, 91,103,104,10712. Gray 19, 26, 47, 5913. Black 17, 40, 70, 7914. Maroon 48, 5315. LightGreen 25, 32, 35, 60, 66, 71, 73,10516. Cyan 10,10217. Yellow 2, 22, 81, 9018. Green 14, 58, 61, 8319. Pink 4, 15, 46, 52, 77, 78,109,11020. Blue 7, 8, 27, 4121. Fuchsia 6, 50, 67, 9622. White 82, 84, 95, 9723. Orange 31, 8024. Purple 16, 29, 98,10825. NavyBlue 38, 72, 86, 8726. TealBlue 37, 4527. OliveGreen 28, 62, 93,11128. Gray 34, 49, 56,10029. Black 69, 94
Large graph can be generated from words in a dictionary. We constructed a graph inwhich two words are connected iff one can be obtained from the other by changing sin-gle character (e. g. WORK – WORD) or by adding/deleting one character (e.g. EVER– FEVER). Then we took english words graph-drawing-contest, find all short-est paths between graph and drawing and between drawing and contest, drawthe obtained graph using layers option in Pajek (layers are determined by distance fromdrawing). Additionally we added two puzzles:� one difficult: find shortest paths alone,
28
Figure 22: Graph C98.
� one easy: find only missing words on the paths.
See also: http://vlado.fmf.uni-lj.si/pub/gd/gd98.htm
29
www.att.com/catalog/consumer
www.att.com
www.att.com/att
www.att.com/cmd/custcare
www.att.com/write
www.att.com/worldnet
www.att.com/terms.html
www.att.com/learningnetwork
www.att.com/cgi-bin/ppps.cgi
www.att.com/catalog/small_businesswww.att.com/whatsnew
www.att.com/cgi-bin/bmd_cart.cgi
www.att.com/cmd/jump
www.att.com/catalog
www.att.com/textindex.html
www.att.com/bmd/tollfree
www.att.com/worldnet/wmis
search.att.com
www.att.com/bmd/jump
www.att.com/features
www.att.com/rock
www.att.com/home
Figure23:G
raphA
98,afterexecutingdeletion:
deletewww.att.com->www.att.com/catalog/consumer
(23operations
executed).
30
www.att.com/catalog/consumer
www.att.com
www.att.com/att
www.att.com/write
www.att.com/worldnet
www.att.com/terms.html
www.att.com/cgi-bin/ppps.cgi
www.att.com/catalog/small_businesswww.att.com/whatsnew
www.att.com/cgi-bin/bmd_cart.cgi
www.att.com/cmd/jump
www.att.com/catalog
www.att.com/textindex.html
www.att.com/worldnet/wmis
search.att.com
www.att.com/bmd/jump
www.att.com/features
www.att.com/rock
www.att.com/home
www.att.com/services
www.att.com/net
www.att.com/worldnet/wis/sky/signup.html
www.att.com/bmd/products
www.att.com/news
www.att.com/worldnet/intranet
Figure24:G
raphA
98,afterexecutingdeletion:
deletewww.att.com/whatsnew->www.att.com/catalog/consumer
(38operations
executed).
31
www.att.com/catalog/consumer
www.att.com
www.att.com/att
www.att.com/cmd/custcare
www.att.com/write
www.att.com/worldnet
www.att.com/terms.html
www.att.com/learningnetwork
www.att.com/cgi-bin/ppps.cgi
www.att.com/catalog/small_businesswww.att.com/whatsnew
www.att.com/cgi-bin/bmd_cart.cgi
www.att.com/cmd/jump
www.att.com/catalog
www.att.com/textindex.html
www.att.com/bmd/tollfree
www.att.com/worldnet/wmis
search.att.com
www.att.com/bmd/jump
www.att.com/features
www.att.com/rock
www.att.com/home
www.att.com/services
www.att.com/net
www.att.com/worldnet/wis/sky/signup.html
www.att.com/bmd/products
www.att.com/news
www.att.com/worldnet/intranet
www.att.com/bmd/custcare
www.att.com/cgi-bin/cart.cgi
www.att.com/cmd
www.att.com/cmd/products
www.att.com/speeches
www.att.com/speeches/index96.html
www.att.com/international
www.att.co.uk
www.att.com/business
www.catalog.att.com/cmd/jump
Figure25:G
raphA
98,afteralladditions/deletionsdone
(65operations
executed).
32
1
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Tag 1
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Figure26:G
raphB
98(firstprize).
33
graph
drawing
contestPajek
Figure27:G
raphD
98:Difficultpuzzle.
34
graph
pine
pipe
rape
ripe
aping
grape
grate gripe
graphs
grates
gratin
raping
rating
craping
crating
draping
grating
drawing
cong
cove
pong
covercovet
covert
content
convent
contestPajek
Figure28:
Graph
D98:E
asypuzzle.
35
graph
pine
ping
pipe
rape
ripe
aping
grape
grate gripegrapes
graphs
grates
gratin
gratis
raping
rating
craping
crating
draping
grating
drawing
cone
cong
cove
pong
covercovet
covert
content
convent
convert
contestPajek
Figure29:G
raphD
98:Solution.
36
Layouts for Graph Drawing Contest 1999
In 1999 Graph Drawing Conference was helt in Stirin (Czeck Republic) and the contestwas organised by Franz Brandenburg, Michael Juenger, Joe Marks, Petra Mutzel, and FalkSchreiber. Rules and data are described at:
http://www.ms.mff.cuni.cz/acad/kam/conferences/GD99/contest/rules.html
All work was done using our program package Pajek, which is freely available at:http://vlado.fmf.uni-lj.si/pub/networks/pajek/
Graph A99
Graph data were transformed to Pajek format, which enables to handle graph changes overtime. The following coding of actors is used:
� Shapes
– circle: =f= female
– triangle: =m= male
– yellow box: =b= female+male (Ernst+Lisl Wiesenhuber)
– green box: =a= women+grandchildren (Julia von der Marwitz)
– black diamond: =w= widowed
– pink diamond: =d= divorced marriage
– orange diamond: =m= still existing marriage
– empty: =i= invisible node (white)
� Sizes
– 0.8 - big
– 0.4 - small
– 0.6 - artificial
� Colors
– =y= unactive characters (yellow)
– =a= 2 persons in 2 different colors (green)
– =b= active characters (blue)
– =d= divorced marriage (pink)
37
– =w= characters that never showed up personally (white)
– =m= still existing marriage (orange)
– =g= already dead characters (grey)
– =w= widowed (black)� Border widths
– =p= picture - border width = 2
– =s= symbol - border width = 0.5
Drawing of the current situation We started the drawing using the layout obtainedby Kamada-Kawai spring embedder. Later we used manual editing to arrange them onrectangular net.
Development of the graph over time We used the Pajek option for drawing graphsin different time points. Only time points where at least one vertex or one line changesaccording to last layout were drawn (e.g. 1, 2, 4, 5,...). After each change time the layout ofthe new graph was optimized starting with the previous positions.
The layout was awarded the first prize.
Graph B99
We used eigenvectors approach and computed eigenvectors of Laplacean matrix that corre-spond to the 1st, 2nd and 5th largest eigenvalue. No additional manual editing was used onthe obtained spatial picture. Suitable view was selected to get planar EPS picture. Picturewas exported to formats for the following 3D viewers: VRML (CosmoPlayer), kinemages(Mage), and MDLMOLfile (Chime).
The layout was awarded the second prize.
Graph C99
We started the drawing using the layout obtained by Fruchterman-Reingold spring embed-der. Later we used manual editing to maximize ’rectangularity’ and made some displace-ments to accommodate for different sizes of nodes.
See: http://vlado.fmf.uni-lj.si/pub/gd/gd99.htm .The complete report of the contest is available in [8].
38
Rosi Koch
Zorro Franz Josef Pichelsteiner
Onkel Franz Franz Wittich
Gung Pahm Kien
Urzula Wienicki
Gabi Zenker-geb.Skawowski
Phil Seegers
Hans Wilhelm Huelsch
Hajo Scholz
Olli Klatt
Erich-Schiller
Helga Beimer Schiller
Hans Beimer Anna Ziegler
Andy Zenker
Berta Griese
Lisa Hoffmeister
Marion Beimer
Klaus Beimer
Dr. Eva-Maria Sperling
Boris Ecker
Valerie Ecker
Iffi Zenker
Momo Sperling
Dr. Ahmet Dagdelen
Else Kling
Paolo Varese
Dani Schmitz
Philipp Sperling
Tanja Schildknecht-Dressler
Dr. Ludwig Dressler
Mary KlingOlaf Kling
Fausto Rossini
Frank DresslerElena Sarikakis
Isolde Pavarotti
Kaethe Georg Eschweiler
Carsten Floeter Theo Klages
Beate Sarikakis
Vasily Sarikakis
Rolf Sattler Bolle Guenther Bollmann
Hilmar Eggers
Wilhelm Loesch
Marlene Schmitt
Friedemann Traube
Wanda Winicki
Pat Wolffson
Winifred Snyder
Irina Winicki
Sophie ZieglerTom Ziegler
Sarah Ziegler
Paula Madalena Francesca Winicki
Canan Dagdelen
Herr Panowski
Giovanna Varese
Marcella Varese
Nico Zenker
Gina Varese
Chromo Hoyonda
Alfredo
Francesco
Professor Dr. Rudolf Tenge-Wegemmann
Frau Horowitz
Harry
Zeki Kurtalan
Fritjof Lothar Boedefeld
Gundel Koch
Dr. Otto Pichelsteiner
Leo Klamm
Rita Bassermann
Simone Fitz
Dora Wittich
Martha
Bruno Skabowski
Sue
Theresa Zenker
Inge Kling
Ernst+Lisl Wiesenhuber
gesch.Skabowski*19.10.1927
*09.08.1963
*24.07.1913
*23.10.1958
*10.02.1963
verw.Zimmermann*23.05.1960
*14.04.1961
*29.02.1952
*09.06.1944
*06.01.1976
*23.07.1944
geb.Wittich*24.03.1940
*03.10.1943 geb.Jenner*14.07.1959
*03.07.1947
geb.Nolte*25.06.1941
*19.10.1981
*21.05.1969
*17.10.1078
*06.08.1947
*17.06.1965
geb.Zenker*08.10.1975
*19.08.1978
*01.04.1975
*14.05.1922
*14.09.1977
geb.Schildknecht*19.06.1970
*27.06.1933
geb.Dankor*30.01.1969*10.11.1955
*31.10.1966*08.11.1939
verw.Panowak*27.11.1936
*05.03.1966
geb.Floeter*17.08.1970
*14.02.1963
*02.07.1942
geb.Kollin*17.07.1938
*05.05.1972
*18.10.1990
*25.07.1991*27.07.1989
*22.10.1987
*29.08.1996
*12.05.1994*25.10.1970
*06.04.1940
*22.05.1962
+1964
Unbekannter_Russe
+1986
*1947+1964
*1955+1965
*19.09.1996
*10.05.1968+29.08.1991
*30.01.1992
*14.11.1991
*1969+1986
*19.04.1996
*13.03.1994
*18.07.1996
*24.07.1997
*26.11.1987+18.08.1996Figure30:G
raphA
99,currentsituation.
39
Lydia Nolte
Gung Pahm Kien
Gabi Zenker-geb.Skawowski
Helga Beimer Schiller
Hans Beimer
Berta Griese
Marion Beimer
Benny BeimerKlaus Beimer
Franz Schildknecht
Henny Schildknecht
Stefan Nossek
Egon Kling
Else Kling
Tanja Schildknecht-DresslerDr. Ludwig Dressler
Vasily Sarikakis
Chris Barnsteg
Elfie Kronmayr
Sigi Kronmayr
Philo Bennarsch
Joschi Bennarsch
Paul Nolte
Theo Nolte
Lydia Nolte
Gung Pahm Kien
Gabi Zenker-geb.Skawowski
Helga Beimer Schiller
Hans Beimer
Berta Griese
Marion Beimer
Benny BeimerKlaus Beimer
Franz Schildknecht
Henny Schildknecht
Stefan Nossek
Egon Kling
Else Kling
Tanja Schildknecht-DresslerDr. Ludwig Dressler
Elisabeth Dressler
Carsten Floeter
Vasily Sarikakis
Chris Barnsteg
Elfie Kronmayr
Sigi Kronmayr
Gottlieb Griese
Philo Bennarsch
Joschi Bennarsch
Paul Nolte
Theo Nolte
Herr Floether Der Englaender
Lydia Nolte
Gung Pahm Kien
Gabi Zenker-geb.Skawowski
Helga Beimer Schiller
Hans Beimer
Berta Griese
Marion Beimer
Benny BeimerKlaus Beimer
Franz Schildknecht
Henny Schildknecht
Stefan Nossek
Egon Kling
Else Kling
Tanja Schildknecht-DresslerDr. Ludwig Dressler
Elisabeth Dressler
Frank Dressler
Carsten Floeter
Vasily Sarikakis
Chris Barnsteg
Elfie Kronmayr
Sigi Kronmayr
Gottlieb Griese
Meike Schildknecht Philo Bennarsch
Joschi Bennarsch
Paul Nolte
Theo Nolte
Herr Floether Der Englaender
Figure 31: Graph A99, time points 5, 6 and 7 (first prize).
40
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Figure32:
Graph
B99
(secondprize).
41
Figure 33: Graph B99 – general view.
42
Figure 34: Graph B99 – different views.
43
XANTHOSINE NUCLEOTIDE
RIBONUCLEIC ACIDDEOXYRIBONUCLEIC ACID
DEOXYGUANOSINE NUCLEOTIDE GUANOSINE NUCLEOTIDE
INOSINE NUCLEOTIDEADENOSINE NUCLEOTIDEDEOXYADENOSINE NUCLEOTIDE
GLUCOSE
TRIACYLGLYCEROLS ISOLEUCINE
CYTOCHROMES
URONIC ACIDS
CELLULOSE
RIBOSE 5-PNDPGLUCOSESUCROSE
FRUCTOSE
GLYCOGEN
STARCH
AMINO SUGARS
ERYTHROSE 4-P
PENTOSES
P-RIBOSYLPP
ASCORBATE
GLUCOSE 6-P
HISTIDINE
PHENYLALANINE
TYROSINE
TRYPTOPHAN
GLYCERALDEHYDE 3-P
CHORISMATE
ASPARTATE
ARGININE
LEUCINE
ALANINE
COBALAMIN
PROTOPORPHYRIN IX
CHLOROPHYLL
HEME
PLANT STEROIDS ISOPRENOIDS
PHOSPOLIPIDS
FATTY ACIDS
3-P GLYCERATE
LIGNIN
ACETYL-CoA
SUCCINATE
CITRATE
PYRUVATE
GLYCEROL
FUMARATE2-OXOGLUTERATE
OXALOACETATE
GLYOXYLATE
HORMONES
FRUCTOSE 6-P
VALINE
SERINE
GLYCINE
CHOLESTEROL
STEROID HORMONES
BILE ACIDS
GLUTAMATE
PROLINE HYDROXYPROLINE
ORNITHINE
LYSINE
THREONINE
METHIONINE
CYSTEINE
UREA
5-AMINOLEVULINATE BILE PIGMENTS
Degradation
Degradation
NAD+
CYTIDINE NUCLEOTIDE
RIBONUCLEIC ACID
DEOXYRIBONUCLEIC ACID
DEOXYCYTIDINE NUCLEOTIDE
URIDINE NUCLEOTIDE DEOXYURIDINE NUCLEOTIDE
DEOXYTHYMIDINE NUCLEOTIDE
Figure35:G
raphC
99.
44
XANTHOSINE NUCLEOTIDE
RIBONUCLEIC ACIDDEOXYRIBONUCLEIC ACID
DEOXYGUANOSINE NUCLEOTIDE GUANOSINE NUCLEOTIDE
INOSINE NUCLEOTIDEADENOSINE NUCLEOTIDEDEOXYADENOSINE NUCLEOTIDE
GLUCOSE
TRIACYLGLYCEROLS ISOLEUCINE
CYTOCHROMES
URONIC ACIDS
CELLULOSE
RIBOSE 5-PNDPGLUCOSE
SUCROSE
FRUCTOSE
GLYCOGEN
STARCH
AMINO SUGARS
ERYTHROSE 4-P
PENTOSES
P-RIBOSYLPP
ASCORBATE
GLUCOSE 6-P
HISTIDINE
PHENYLALANINE
TYROSINE
TRYPTOPHAN
GLYCERALDEHYDE 3-P
CHORISMATE
ASPARTATE
ARGININE
LEUCINE
ALANINE
COBALAMIN
PROTOPORPHYRIN IX
CHLOROPHYLL
HEME
PLANT STEROIDS ISOPRENOIDS
PHOSPOLIPIDS
FATTY ACIDS
3-P GLYCERATE
LIGNIN
ACETYL-CoA
SUCCINATE
CITRATE
PYRUVATE
GLYCEROL
FUMARATE2-OXOGLUTERATE
OXALOACETATE
GLYOXYLATE
HORMONES
FRUCTOSE 6-P
VALINE
SERINE
GLYCINE
CHOLESTEROL
STEROID HORMONES
BILE ACIDS
GLUTAMATE
PROLINE HYDROXYPROLINE
ORNITHINE
LYSINE
THREONINE
METHIONINE
CYSTEINE
UREA
5-AMINOLEVULINATE BILE PIGMENTS
Degradation
Degradation
NAD+
CYTIDINE NUCLEOTIDE
RIBONUCLEIC ACID
DEOXYRIBONUCLEIC ACID
DEOXYCYTIDINE NUCLEOTIDE
URIDINE NUCLEOTIDE DEOXYURIDINE NUCLEOTIDE
DEOXYTHYMIDINE NUCLEOTIDE
Figure36:G
raphC
99-orthogonallayout.
45
Layouts for Graph Drawing Contest 2000
In 2000 Graph Drawing Conference was helt in Colonial Williamsburg (USA) and the con-test was organised by Franz Brandenburg. Rules and data are described at:
http://www.infosun.fmi.uni-passau.de/GD2000/index.html
Graph A00
Graph A00 was proposed by M. Himsolt.First we found out that graph consists of 26 weakly connected components. After re-
moving loops from the graph we got acyclic graph. On the acyclic graph we used standardalgorithms to compute layers and position vertices into layers in order to minimize totallength of lines. Some manual repositioning of vertices was used to avoid some line cross-ings. Vertices having loops are drawn as ellipses other as rectangles. Since graph consists ofseveral components and labels are very small, some additional layouts of parts of network(top, middle and bottom) containing some components are shown.
We also produced pictures of this graph in Scalable Vector Graphics (SVG) formatbesides EPS pictures (see http://vlado.fmf.uni-lj.si/pub/gd/gd00.htm).
Graph B00
Graphs B00-A and B00-B were proposed by Ulrik Brandes.The essential part of both graphs A and B are the green vertices. But there are to many
arcs among them to produce a clear picture.We first tried with circular presentation. To reveal internal structure of green subgraph
and to determine the ordering of vertices on the circle we computed�'¡
on the green sub-graph and applied TSP (Travelling Salesman Problem) algorithm on this matrix.
�Y¡3¢ £ ¤N¥§¦¨� © ª ¢ £¦+« ª ¢ ¥§¦ ©© ª ¢ £¦+¬ ª ¢ ¥§¦ © (1)
ª ¢ ¥§¦is the neighborhood of vertex
¥®°¯:
ª ¢ ¥�¦��²±�£³³¯�´�¢ ¥®´-£¦µ>¶¸·(«
denotes the symmetric difference,¬
denotes union)Since there can exist different clusters inside the green set of vertices we extended the�H¡matrix with some additional vertices with equal distance to all green vertices. Some
vertices were repositioned manually according to connections to yellow and blue verticeson the circular net. From obtained pictures we can see that neighbouring vertices havesimilar patterns of arcs. Vertices having loops are drawn as boxes (vertices 5 and 11 ingraph A) other as circles. Different gray colors are used to show the frequency of contact:
46
� Black: 1 - weekly
� 75% Gray: 2 - biweekly
� 50% Gray: 3 - monthly
� 25% Gray: 4 - quarterly
The ordering of green vertices obtained by TSP algorithm we used also in matrix repre-sentation of graphs A and B. It seems that the matrix representation is more appropriate fordense (parts of) graphs. In the matrix representation the same shadowing is used as in thegraph layout.
The layout was awarded the first prize.The complete report of the contest is available in [9].
47
basic_fstream<char, char_traits<char>>
basic_iostream<char, char_traits<char>>basic_istream<char, char_traits<char>> basic_ios<char, char_traits<char>>
ios_base
locale
basic_ostream<char, char_traits<char>>
basic_filebuf<char, char_traits<char>>
basic_streambuf<char, char_traits<char>>
BrokenRelationException
BuildExceptionlist<string, allocator<PropertyName>>
allocator<PropertyName>
iterator
const_iterator
EntryNotFoundException
FileNotInProjectFileException
Exception
ParentScopeNotFoundException
UnimportantOperationException
UnimportantStatementException
__non_rtti_object bad_typeid
exception
codecvt<wchar_t, char, mbstate_t>
codecvt_base
facet
codecvt<char, char, state_type>
domain_error
logic_errorinvalid_argument
length_error
out_of_range
overflow_error
runtime_errorrange_error
underflow_error
failure
CppModel Model
list<Relation*, allocator<Relation*>>
allocator<Relation*>
iterator const_iterator
set<PropertyName, less<string>, allocator<string>>
allocator<string>
ProjectFile map<string, SectionContents, less<string>, allocator<SectionContents>>allocator<SectionContents>
value_compare
SectionNotFound
VariableNotFound
bad_alloc
bad_cast
bad_exception
basic_istream<wchar_t, char_traits<wchar_t>>basic_ios<wchar_t, char_traits<wchar_t>>
basic_ostream<wchar_t, char_traits<wchar_t>>
num_put<char, _Iter>
numpunct<char>
_Locimp
Array
TypeRef
Type
Entity
Element
Object
SCPos
Class
Record
CppModelFactory ModelFactory
Pointer
PointerToMemberQualifiedType
Struct
TypeDef
Union
ElementType
set<ElementType*, less<ElementType*>, allocator<ElementType*>>
allocator<ElementType*>
ILManager map<ILInstanceKey, ILInstance, less<ILInstanceKey>, allocator<ILInstance>>
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value_compare
Logmap<int, string, less<int>, allocator<string>>
value_compare
map<string, int, less<string>, allocator<int>>
allocator<int>
value_compare
Measurement map<string, int, less<PropertyName>, allocator<int>> value_compare
Project
set<string, less<string>, allocator<string>>
list<string, allocator<string>> iterator const_iterator
map<string, SourceFile, less<string>, allocator<SourceFile>>
allocator<SourceFile>
value_compare
_Tree<TypeRefHack, value_type, _Kfn, LessByReferencedType, allocator<TypeRefHack>>
allocator<TypeRefHack>
iterator const_iterator
_Tree<TypeRefHack, value_type, _Kfn, LessByReferencedType, allocator<TypeRefHack>> iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<SectionContents>> iterator const_iterator
_Tree<Cell*, value_type, _Kfn, less<Cell*>, allocator<Cell*>> allocator<Cell*>
_Tree<Cell*, value_type, _Kfn, less<Cell*>, allocator<Cell*>> iterator
const_iterator
basic_string<char, char_traits<char>, allocator<char>> allocator<char>
list<Cell*, allocator<Cell*>> iterator const_iterator
stack<Block*, deque<Block*, allocator<Block*>>> deque<Block*, allocator<Block*>> iterator const_iterator
allocator<Block*>
map<Cell*, Cell*, less<Cell*>, allocator<Cell*>> value_compare
multiset<TypeRefHack, LessByReferencedType, allocator<TypeRefHack>>
iterator
Builtin
ClassTemplate
Template
Function
Routine
FunctionTemplate
InNamespace
InScope
Relation
InRecordScope
Member
Field
Method
RoutineType
StaticDataMemberTemplate
Variable
Property
list<PropertyValue, allocator<PropertyValue>>
allocator<PropertyValue>
iterator const_iterator
PropertyValue
_Tree<int, value_type, _Kfn, less<int>, allocator<string>>iterator
_Tree<int, value_type, _Kfn, less<int>, allocator<string>> iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<int>>iterator const_iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<int>> iterator
_Tree<RoutineTypeHack, value_type, _Kfn, LessByParamTypes, allocator<RoutineTypeHack>>
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iterator const_iterator
_Tree<PropertyName, value_type, _Kfn, less<string>, allocator<string>>
_Tree<PropertyName, value_type, _Kfn, less<string>, allocator<string>>iterator
_Tree<ElementType*, value_type, _Kfn, less<ElementType*>, allocator<ElementType*>>
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iterator const_iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<string>> iterator
const_iterator_Tree<string, value_type, _Kfn, less<string>, allocator<string>> iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<ElementType*>>
_Tree<string, value_type, _Kfn, less<string>, allocator<ElementType*>> iterator
const_iterator
_Tree<ILInstanceKey, value_type, _Kfn, less<ILInstanceKey>, allocator<ILInstance>>
_Tree<ILInstanceKey, value_type, _Kfn, less<ILInstanceKey>, allocator<ILInstance>> iteratorconst_iterator
_Tree<string, value_type, _Kfn, less<ILInstanceKey>, allocator<int>>
_Tree<string, value_type, _Kfn, less<ILInstanceKey>, allocator<int>>iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<string>> iteratorconst_iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<string>>iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<SourceFile>>allocator<SourceFile>
iterator const_iterator
_Tree<ILInstanceKey, value_type, _Kfn, less<string>, allocator<ILInstance>>
_Tree<ILInstanceKey, value_type, _Kfn, less<string>, allocator<ILInstance>>iterator
_Tree<STD_Ptr<Cell>, value_type, _Kfn, CellLessByElementID, allocator<STD_Ptr<Cell>>> allocator<STD_Ptr<Cell>>
_Tree<STD_Ptr<Cell>, value_type, _Kfn, CellLessByElementID, allocator<STD_Ptr<Cell>>>iterator const_iterator
_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<PropertyName>> iterator
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_Tree<int, value_type, _Kfn, less<int>, allocator<PropertyName>> iterator
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_Tree<string, value_type, _Kfn, less<PropertyName>, allocator<int>> iterator
_Tree<string, value_type, _Kfn, less<PropertyName>, allocator<int>> iterator
_Tree<void*, value_type, _Kfn, less<void*>, allocator<Entity*>>allocator<Entity*>
iterator
const_iterator_Tree<void*, value_type, _Kfn, less<void*>, allocator<Entity*>>iterator
_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<Property>>allocator<Property>
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const_iterator_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<Property>>
iterator
_Tree<ILInstanceKey, value_type, _Kfn, less<PropertyName>, allocator<ILInstance>>
_Tree<ILInstanceKey, value_type, _Kfn, less<PropertyName>, allocator<ILInstance>>iterator
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const_iterator
list<Entity*, allocator<Entity*>> iterator const_iterator
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list<Element*, allocator<Element*>>
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iterator const_iterator
list<TempResult, allocator<TempResult>>
allocator<TempResult>
iterator const_iterator
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list<STD_Ptr<TemplateParameter>, allocator<STD_Ptr<TemplateParameter>>>
allocator<STD_Ptr<TemplateParameter>>
iterator const_iterator
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list<BaseClass*, allocator<BaseClass*>>
allocator<BaseClass*>
iterator const_iterator
allocator<BaseClass*>
list<Constant*, allocator<Constant*>>
allocator<Constant*>
iterator const_iterator
list<Actual, allocator<Actual>>
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reverse_iterator<iterator, value_type, reference, reference*, difference_type> iteratorconst_iterator
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map<string, ElementType*, less<string>, allocator<ElementType*>> value_compare
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map<ILInstanceKey, ILInstance, less<string>, allocator<ILInstance>>value_compare
map<int, string, less<int>, allocator<PropertyName>> value_compare
map<void*, Entity*, less<void*>, allocator<Entity*>>value_compare
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set<STD_Ptr<Cell>, CellLessByElementID, allocator<STD_Ptr<Cell>>>
set<PropertyName, less<PropertyName>, allocator<PropertyName>>
set<PropertyName, less<string>, allocator<PropertyName>>
vector<_Bool, _Bool_allocator>
ConcretePrimitiveQuery
PrimitiveQuery
Query
list<ColumnDef, allocator<ColumnDef>>allocator<ColumnDef>
iterator const_iteratorColumnDef
DummyRelation
EntitiesByTypeQuery
RelationsByTypeQuery
iterator
iterator
iterator
iterator
Accessor
Block list<STD_Ptr<Block>, allocator<STD_Ptr<Block>>>allocator<STD_Ptr<Block>>
iterator const_iterator
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STD_Ptr<Block>
CallFieldAccess
Friend
HasType
Inheritance
LocalVariableOfType
LocallyUsedType
NameSpace
Parameter
ReturnType
TemplateInstance
TypeUsedInTypeRef
basic_streambuf<wchar_t, char_traits<wchar_t>>
reverse_iterator<const_iterator, value_type, const_reference, const_reference*, difference_type>
ParallelQuerylist<Query*, allocator<Query*>>
allocator<Query*>iterator const_iterator
RecursiveQuery
Scopemultiset<STD_Ptr<Entity>, LessByName, allocator<STD_Ptr<Entity>>> allocator<STD_Ptr<Entity>>
set<STD_Ptr<Scope>, less<STD_Ptr<Scope>>, allocator<STD_Ptr<Scope>>> allocator<STD_Ptr<Scope>>
SerialQuery
Constant
TemplateParameter_Tree<STD_Ptr<Scope>, value_type, _Kfn, less<STD_Ptr<Scope>>, allocator<STD_Ptr<Scope>>> iterator const_iterator
_Tree<STD_Ptr<Entity>, value_type, _Kfn, LessByName, allocator<STD_Ptr<Entity>>> iterator const_iterator
Figure37:
Com
pletelayoutofH
imsoltgraph
A00.
48
Array
TypeRef
Type
Entity
Element
Object
SCPos
Class
Record
Pointer
PointerToMember
QualifiedType
Struct
TypeDef
Union
Builtin
ClassTemplate
Template
Function
Routine
FunctionTemplate
InNamespace
InScope
Relation
InRecordScope
Member
Field
Method
RoutineType
StaticDataMemberTemplate
Variable
ConcretePrimitiveQuery
PrimitiveQuery
Query
list<ColumnDef, allocator<ColumnDef>>
allocator<ColumnDef>
iterator const_iterator
ColumnDef
DummyRelation
EntitiesByTypeQuery
RelationsByTypeQuery
Accessor
Blocklist<STD_Ptr<Block>, allocator<STD_Ptr<Block>>>
allocator<STD_Ptr<Block>>
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allocator<STD_Ptr<Block>>
STD_Ptr<Block>
STD_Ptr<Block>
Call
FieldAccess
Friend
HasType
Inheritance
LocalVariableOfType
LocallyUsedType
NameSpace
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ReturnType
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TypeUsedInTypeRef
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list<Query*, allocator<Query*>>
allocator<Query*>
iterator const_iterator
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Scope
multiset<STD_Ptr<Entity>, LessByName, allocator<STD_Ptr<Entity>>>allocator<STD_Ptr<Entity>>
set<STD_Ptr<Scope>, less<STD_Ptr<Scope>>, allocator<STD_Ptr<Scope>>> allocator<STD_Ptr<Scope>>
SerialQuery
Constant
TemplateParameter
_Tree<STD_Ptr<Scope>, value_type, _Kfn, less<STD_Ptr<Scope>>, allocator<STD_Ptr<Scope>>>
iterator const_iterator
_Tree<STD_Ptr<Entity>, value_type, _Kfn, LessByName, allocator<STD_Ptr<Entity>>>iterator const_iterator
Figure38:
UpperpartofH
imsoltgraph
A00.
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BrokenRelationException
BuildExceptionlist<string, allocator<PropertyName>>
allocator<PropertyName>
iterator
const_iterator
EntryNotFoundException
ParentScopeNotFoundException
UnimportantOperationException
UnimportantStatementException
CppModel Model
list<Relation*, allocator<Relation*>>
allocator<Relation*>
iterator const_iterator
set<PropertyName, less<string>, allocator<string>>
allocator<string>
ProjectFile map<string, SectionContents, less<string>, allocator<SectionContents>>allocator<SectionContents>
value_compare
ElementType
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ILManager map<ILInstanceKey, ILInstance, less<ILInstanceKey>, allocator<ILInstance>>
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Log
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Measurement map<string, int, less<PropertyName>, allocator<int>>value_compare
Project
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iterator
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allocator<ElementType*>
iterator const_iterator
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const_iterator_Tree<string, value_type, _Kfn, less<string>, allocator<string>>
iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<ElementType*>>
_Tree<string, value_type, _Kfn, less<string>, allocator<ElementType*>> iterator
const_iterator
_Tree<ILInstanceKey, value_type, _Kfn, less<ILInstanceKey>, allocator<ILInstance>>
_Tree<ILInstanceKey, value_type, _Kfn, less<ILInstanceKey>, allocator<ILInstance>>iterator
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_Tree<string, value_type, _Kfn, less<string>, allocator<string>>
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_Tree<string, value_type, _Kfn, less<string>, allocator<SourceFile>>
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_Tree<ILInstanceKey, value_type, _Kfn, less<string>, allocator<ILInstance>>
_Tree<ILInstanceKey, value_type, _Kfn, less<string>, allocator<ILInstance>>iterator
_Tree<STD_Ptr<Cell>, value_type, _Kfn, CellLessByElementID, allocator<STD_Ptr<Cell>>> allocator<STD_Ptr<Cell>>
_Tree<STD_Ptr<Cell>, value_type, _Kfn, CellLessByElementID, allocator<STD_Ptr<Cell>>>iterator const_iterator
_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<PropertyName>> iterator
const_iterator_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<PropertyName>>
iterator
_Tree<int, value_type, _Kfn, less<int>, allocator<PropertyName>> iterator
_Tree<int, value_type, _Kfn, less<int>, allocator<PropertyName>> iterator
_Tree<string, value_type, _Kfn, less<PropertyName>, allocator<int>> iterator
_Tree<string, value_type, _Kfn, less<PropertyName>, allocator<int>> iterator
_Tree<void*, value_type, _Kfn, less<void*>, allocator<Entity*>>
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list<TempResult, allocator<TempResult>>
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map<string, ElementType*, less<string>, allocator<ElementType*>> value_compare
map<string, int, less<ILInstanceKey>, allocator<int>> value_compare
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map<ILInstanceKey, ILInstance, less<string>, allocator<ILInstance>>value_compare
map<int, string, less<int>, allocator<PropertyName>> value_compare
map<void*, Entity*, less<void*>, allocator<Entity*>>
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map<PropertyName, Property, less<PropertyName>, allocator<Property>>
value_compare
map<ILInstanceKey, ILInstance, less<PropertyName>, allocator<ILInstance>>value_compare
set<STD_Ptr<Cell>, CellLessByElementID, allocator<STD_Ptr<Cell>>>
set<PropertyName, less<PropertyName>, allocator<PropertyName>>
set<PropertyName, less<string>, allocator<PropertyName>>
iterator
iterator
iterator
iterator
Figure39:M
iddlepartofH
imsoltgraph
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basic_fstream<char, char_traits<char>>
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ios_base
locale
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basic_filebuf<char, char_traits<char>>
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__non_rtti_object
bad_typeid
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codecvt<wchar_t, char, mbstate_t>
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codecvt<char, char, state_type>
domain_error
logic_error
invalid_argument
length_error
out_of_range
overflow_error
runtime_errorrange_error
underflow_error
failure
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bad_cast
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basic_istream<wchar_t, char_traits<wchar_t>>
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CppModelFactory ModelFactory
_Tree<TypeRefHack, value_type, _Kfn, LessByReferencedType, allocator<TypeRefHack>>
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list<Constant*, allocator<Constant*>>
allocator<Constant*>
iterator const_iterator
list<Actual, allocator<Actual>>
allocator<Actual>
iterator const_iterator
reverse_iterator<iterator, value_type, reference, reference*, difference_type>iterator
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reference
multiset<RoutineTypeHack, LessByParamTypes, allocator<RoutineTypeHack>>
vector<_Bool, _Bool_allocator>
basic_streambuf<wchar_t, char_traits<wchar_t>>
reverse_iterator<const_iterator, value_type, const_reference, const_reference*, difference_type>
Figure40:B
ottompartofH
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8687
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9192
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99
Figure 41: Graph B00-A - circular layout (first prize).
52
0
1
2
3
4
5
6
7
8
9
1011
12
13
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96
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100
Figure 42: Graph B00-B - circular layout.
53
3 Green 13 Green 11 Green 1 Green 0 Green 17 Green 9 Green 2 Green 12 Green 81 Green 5 Green 15 Green 14 Green 18 Green 10 Green 16 Green 4 Green 8 Green 7 Green 6 Green 92 Blue 91 Blue 82 Blue 83 Blue 84 Blue 85 Blue 86 Blue 87 Blue 88 Blue 93 Blue 89 Blue 96 Blue 97 Blue 98 Blue 99 Blue 90 Blue 94 Blue 95 Blue 78 Yellow 64 Yellow 25 Yellow 32 Yellow 74 Yellow 26 Yellow 27 Yellow 52 Yellow 55 Yellow 23 Yellow 60 Yellow 62 Yellow 24 Yellow 20 Yellow 77 Yellow 46 Yellow 61 Yellow 80 Yellow 28 Yellow 39 Yellow 34 Yellow 43 Yellow 72 Yellow 22 Yellow 57 Yellow 69 Yellow 70 Yellow 65 Yellow 66 Yellow 67 Yellow 31 Yellow 37 Yellow 42 Yellow 71 Yellow 19 Yellow 41 Yellow 53 Yellow 59 Yellow 73 Yellow 29 Yellow 79 Yellow 40 Yellow 21 Yellow 36 Yellow 48 Yellow 49 Yellow 50 Yellow 51 Yellow 58 Yellow 68 Yellow 44 Yellow 45 Yellow 54 Yellow 75 Yellow 33 Yellow 63 Yellow 56 Yellow 30 Yellow 76 Yellow 47 Yellow 38 Yellow 35 Yellow
3 G
reen
13
Gre
en
11 G
reen
1
Gre
en
0 G
reen
17
Gre
en
9 G
reen
2
Gre
en
12 G
reen
81
Gre
en
5 G
reen
15
Gre
en
14 G
reen
18
Gre
en
10 G
reen
16
Gre
en
4 G
reen
8
Gre
en
7 G
reen
6
Gre
en
92 B
lue
91 B
lue
82 B
lue
83 B
lue
84 B
lue
85 B
lue
86 B
lue
87 B
lue
88 B
lue
93 B
lue
89 B
lue
96 B
lue
97 B
lue
98 B
lue
99 B
lue
90 B
lue
94 B
lue
95 B
lue
78 Y
ello
w
64 Y
ello
w
25 Y
ello
w
32 Y
ello
w
74 Y
ello
w
26 Y
ello
w
27 Y
ello
w
52 Y
ello
w
55 Y
ello
w
23 Y
ello
w
60 Y
ello
w
62 Y
ello
w
24 Y
ello
w
20 Y
ello
w
77 Y
ello
w
46 Y
ello
w
61 Y
ello
w
80 Y
ello
w
28 Y
ello
w
39 Y
ello
w
34 Y
ello
w
43 Y
ello
w
72 Y
ello
w
22 Y
ello
w
57 Y
ello
w
69 Y
ello
w
70 Y
ello
w
65 Y
ello
w
66 Y
ello
w
67 Y
ello
w
31 Y
ello
w
37 Y
ello
w
42 Y
ello
w
71 Y
ello
w
19 Y
ello
w
41 Y
ello
w
53 Y
ello
w
59 Y
ello
w
73 Y
ello
w
29 Y
ello
w
79 Y
ello
w
40 Y
ello
w
21 Y
ello
w
36 Y
ello
w
48 Y
ello
w
49 Y
ello
w
50 Y
ello
w
51 Y
ello
w
58 Y
ello
w
68 Y
ello
w
44 Y
ello
w
45 Y
ello
w
54 Y
ello
w
75 Y
ello
w
33 Y
ello
w
63 Y
ello
w
56 Y
ello
w
30 Y
ello
w
76 Y
ello
w
47 Y
ello
w
38 Y
ello
w
35 Y
ello
w
Figure 43: Matrix representation of graph B00-A.
54
9 Green 16 Green 17 Green 8 Green 11 Green 13 Green 7 Green 6 Green 2 Green 4 Green 5 Green 19 Green 62 Green 12 Green 18 Green 14 Green 1 Green 0 Green 3 Green 20 Green 15 Green 10 Green 66 Blue 76 Blue 86 Blue 92 Blue 94 Blue 67 Blue 72 Blue 80 Blue 68 Blue 82 Blue 63 Blue 73 Blue 81 Blue 100 Blue 79 Blue 97 Blue 74 Blue 77 Blue 78 Blue 91 Blue 85 Blue 71 Blue 99 Blue 90 Blue 64 Blue 95 Blue 69 Blue 70 Blue 75 Blue 83 Blue 87 Blue 89 Blue 93 Blue 96 Blue 84 Blue 65 Blue 88 Blue 98 Blue 21 Yellow 47 Yellow 33 Yellow 55 Yellow 39 Yellow 30 Yellow 57 Yellow 24 Yellow 32 Yellow 51 Yellow 48 Yellow 26 Yellow 22 Yellow 61 Yellow 49 Yellow 31 Yellow 40 Yellow 56 Yellow 25 Yellow 44 Yellow 60 Yellow 37 Yellow 41 Yellow 23 Yellow 34 Yellow 38 Yellow 45 Yellow 46 Yellow 50 Yellow 58 Yellow 52 Yellow 53 Yellow 43 Yellow 36 Yellow 54 Yellow 28 Yellow 35 Yellow 29 Yellow 59 Yellow 42 Yellow 27 Yellow
9 G
reen
1
6 G
reen
1
7 G
reen
8
Gre
en
11
Gre
en
13
Gre
en
7 G
reen
6
Gre
en
2 G
reen
4
Gre
en
5 G
reen
1
9 G
reen
6
2 G
reen
1
2 G
reen
1
8 G
reen
1
4 G
reen
1
Gre
en
0 G
reen
3
Gre
en
20
Gre
en
15
Gre
en
10
Gre
en
66
Blu
e 7
6 B
lue
86
Blu
e 9
2 B
lue
94
Blu
e 6
7 B
lue
72
Blu
e 8
0 B
lue
68
Blu
e 8
2 B
lue
63
Blu
e 7
3 B
lue
81
Blu
e 10
0 B
lue
79
Blu
e 9
7 B
lue
74
Blu
e 7
7 B
lue
78
Blu
e 9
1 B
lue
85
Blu
e 7
1 B
lue
99
Blu
e 9
0 B
lue
64
Blu
e 9
5 B
lue
69
Blu
e 7
0 B
lue
75
Blu
e 8
3 B
lue
87
Blu
e 8
9 B
lue
93
Blu
e 9
6 B
lue
84
Blu
e 6
5 B
lue
88
Blu
e 9
8 B
lue
21
Yel
low
47
Yel
low
33
Yel
low
55
Yel
low
39
Yel
low
30
Yel
low
57
Yel
low
24
Yel
low
32
Yel
low
51
Yel
low
48
Yel
low
26
Yel
low
22
Yel
low
61
Yel
low
49
Yel
low
31
Yel
low
40
Yel
low
56
Yel
low
25
Yel
low
44
Yel
low
60
Yel
low
37
Yel
low
41
Yel
low
23
Yel
low
34
Yel
low
38
Yel
low
45
Yel
low
46
Yel
low
50
Yel
low
58
Yel
low
52
Yel
low
53
Yel
low
43
Yel
low
36
Yel
low
54
Yel
low
28
Yel
low
35
Yel
low
29
Yel
low
59
Yel
low
42
Yel
low
27
Yel
low
Figure 44: Matrix representation of graph B00-B.
55
3 Green 13 Green 11 Green 1 Green 0 Green 17 Green 9 Green 2 Green 12 Green 81 Green 5 Green 15 Green 14 Green 18 Green 10 Green 16 Green 4 Green 8 Green 7 Green 6 Green 92 Blue 91 Blue 82 Blue 83 Blue 84 Blue 85 Blue 86 Blue 87 Blue 88 Blue 93 Blue 89 Blue 96 Blue 97 Blue 98 Blue 99 Blue 90 Blue 94 Blue 95 Blue 78 Yellow 64 Yellow 25 Yellow 32 Yellow 74 Yellow 26 Yellow 27 Yellow 52 Yellow 55 Yellow 23 Yellow 60 Yellow 62 Yellow 24 Yellow 20 Yellow 77 Yellow 46 Yellow 61 Yellow 80 Yellow 28 Yellow 39 Yellow 34 Yellow 43 Yellow 72 Yellow 22 Yellow 57 Yellow 69 Yellow 70 Yellow 65 Yellow 66 Yellow 67 Yellow 31 Yellow 37 Yellow 42 Yellow 71 Yellow 19 Yellow 41 Yellow 53 Yellow 59 Yellow 73 Yellow 29 Yellow 79 Yellow 40 Yellow 21 Yellow 36 Yellow 48 Yellow 49 Yellow 50 Yellow 51 Yellow 58 Yellow 68 Yellow 44 Yellow 45 Yellow 54 Yellow 75 Yellow 33 Yellow 63 Yellow 56 Yellow 30 Yellow 76 Yellow 47 Yellow 38 Yellow 35 Yellow
3 G
reen
13
Gre
en
11 G
reen
1
Gre
en
0 G
reen
17
Gre
en
9 G
reen
2
Gre
en
12 G
reen
81
Gre
en
5 G
reen
15
Gre
en
14 G
reen
18
Gre
en
10 G
reen
16
Gre
en
4 G
reen
8
Gre
en
7 G
reen
6
Gre
en
92 B
lue
91 B
lue
82 B
lue
83 B
lue
84 B
lue
85 B
lue
86 B
lue
87 B
lue
88 B
lue
93 B
lue
89 B
lue
96 B
lue
97 B
lue
98 B
lue
99 B
lue
90 B
lue
94 B
lue
95 B
lue
78 Y
ello
w
64 Y
ello
w
25 Y
ello
w
32 Y
ello
w
74 Y
ello
w
26 Y
ello
w
27 Y
ello
w
52 Y
ello
w
55 Y
ello
w
23 Y
ello
w
60 Y
ello
w
62 Y
ello
w
24 Y
ello
w
20 Y
ello
w
77 Y
ello
w
46 Y
ello
w
61 Y
ello
w
80 Y
ello
w
28 Y
ello
w
39 Y
ello
w
34 Y
ello
w
43 Y
ello
w
72 Y
ello
w
22 Y
ello
w
57 Y
ello
w
69 Y
ello
w
70 Y
ello
w
65 Y
ello
w
66 Y
ello
w
67 Y
ello
w
31 Y
ello
w
37 Y
ello
w
42 Y
ello
w
71 Y
ello
w
19 Y
ello
w
41 Y
ello
w
53 Y
ello
w
59 Y
ello
w
73 Y
ello
w
29 Y
ello
w
79 Y
ello
w
40 Y
ello
w
21 Y
ello
w
36 Y
ello
w
48 Y
ello
w
49 Y
ello
w
50 Y
ello
w
51 Y
ello
w
58 Y
ello
w
68 Y
ello
w
44 Y
ello
w
45 Y
ello
w
54 Y
ello
w
75 Y
ello
w
33 Y
ello
w
63 Y
ello
w
56 Y
ello
w
30 Y
ello
w
76 Y
ello
w
47 Y
ello
w
38 Y
ello
w
35 Y
ello
w
9 Green 16 Green 17 Green 8 Green 11 Green 13 Green 7 Green 6 Green 2 Green 4 Green 5 Green 19 Green 62 Green 12 Green 18 Green 14 Green 1 Green 0 Green 3 Green 20 Green 15 Green 10 Green 66 Blue 76 Blue 86 Blue 92 Blue 94 Blue 67 Blue 72 Blue 80 Blue 68 Blue 82 Blue 63 Blue 73 Blue 81 Blue 100 Blue 79 Blue 97 Blue 74 Blue 77 Blue 78 Blue 91 Blue 85 Blue 71 Blue 99 Blue 90 Blue 64 Blue 95 Blue 69 Blue 70 Blue 75 Blue 83 Blue 87 Blue 89 Blue 93 Blue 96 Blue 84 Blue 65 Blue 88 Blue 98 Blue 21 Yellow 47 Yellow 33 Yellow 55 Yellow 39 Yellow 30 Yellow 57 Yellow 24 Yellow 32 Yellow 51 Yellow 48 Yellow 26 Yellow 22 Yellow 61 Yellow 49 Yellow 31 Yellow 40 Yellow 56 Yellow 25 Yellow 44 Yellow 60 Yellow 37 Yellow 41 Yellow 23 Yellow 34 Yellow 38 Yellow 45 Yellow 46 Yellow 50 Yellow 58 Yellow 52 Yellow 53 Yellow 43 Yellow 36 Yellow 54 Yellow 28 Yellow 35 Yellow 29 Yellow 59 Yellow 42 Yellow 27 Yellow
9 G
reen
1
6 G
reen
1
7 G
reen
8
Gre
en
11
Gre
en
13
Gre
en
7 G
reen
6
Gre
en
2 G
reen
4
Gre
en
5 G
reen
1
9 G
reen
6
2 G
reen
1
2 G
reen
1
8 G
reen
1
4 G
reen
1
Gre
en
0 G
reen
3
Gre
en
20
Gre
en
15
Gre
en
10
Gre
en
66
Blu
e 7
6 B
lue
86
Blu
e 9
2 B
lue
94
Blu
e 6
7 B
lue
72
Blu
e 8
0 B
lue
68
Blu
e 8
2 B
lue
63
Blu
e 7
3 B
lue
81
Blu
e 10
0 B
lue
79
Blu
e 9
7 B
lue
74
Blu
e 7
7 B
lue
78
Blu
e 9
1 B
lue
85
Blu
e 7
1 B
lue
99
Blu
e 9
0 B
lue
64
Blu
e 9
5 B
lue
69
Blu
e 7
0 B
lue
75
Blu
e 8
3 B
lue
87
Blu
e 8
9 B
lue
93
Blu
e 9
6 B
lue
84
Blu
e 6
5 B
lue
88
Blu
e 9
8 B
lue
21
Yel
low
47
Yel
low
33
Yel
low
55
Yel
low
39
Yel
low
30
Yel
low
57
Yel
low
24
Yel
low
32
Yel
low
51
Yel
low
48
Yel
low
26
Yel
low
22
Yel
low
61
Yel
low
49
Yel
low
31
Yel
low
40
Yel
low
56
Yel
low
25
Yel
low
44
Yel
low
60
Yel
low
37
Yel
low
41
Yel
low
23
Yel
low
34
Yel
low
38
Yel
low
45
Yel
low
46
Yel
low
50
Yel
low
58
Yel
low
52
Yel
low
53
Yel
low
43
Yel
low
36
Yel
low
54
Yel
low
28
Yel
low
35
Yel
low
29
Yel
low
59
Yel
low
42
Yel
low
27
Yel
low
Figure45:M
atrixrepresentation
ofnonem
ptypartofgraphs
B00-A
andB
00-B.
56
Layouts for Graph Drawing Contest 2001
In 2001 Graph Drawing Conference was helt in Vienna and the contest was organised byFranz Brandenburg. Rules and data are described at:
http://www.ads.tuwien.ac.at/gd2001/
Graph A01
In a given set of units¶
(articles, books, works, . . . ) we introduce a ¹�ºT»bºT¼k½ relation ¾À¿¶ÂÁö ľÆÅ�ÇÈÅ cites
Äwhich determines a citation network
¢É¶�¤ ¾ ¦ . A citing relation is usually irreflexive, ÊÄ ¶Ë´�Ì Ä ¾
Ä, and (almost) acyclic, Ê
Ä @¶ ÊÍ IN� ´�Ì Ä ¾8Î
Ä. The citation network is
standardized by adding, if necessary, artificial source vertex � and sink or terminal vertex »and the arc
¢ » ¤ � ¦ (see figure).
An approach to the analysis of citation network is to determine for each unit / arc itsimportance or weight. These values are used afterwards to determine the essential substruc-tures in the network. Hummon and Doreian (1989, 1990) [1, 2, 3] proposed three methodsof assigning weights Ï ´ ¾@Ð IR
�Ñ to arcs:
57
� NPCC method: Ï � ¢ £Ò¤N¥�¦�� © ¾ÔÓ � ¢ £¦ ©1ÕH© ¾ ¢ ¥§¦ ©� Paths count method: Ï ¡3¢ £Ò¤N¥�¦Ö� ª ¢ £Ò¤N¥§¦, where ª ¢ £Ò¤N¥�¦
denotes the number ofdifferent paths from ׳ØoÙ�¾ to ׳Ú1Ûܾ (or from � to » ) through the arc
¢ £Ò¤N¥�¦� SPLC method: ÏÞÝ ¢ £ ¤N¥§¦ß� ªÖà ¢ £Ò¤N¥§¦ , where ªÖà ¢ £Ò¤N¥§¦ equals to ª ¢ £Ò¤N¥�¦
from pathscount method over the network
¢É¶�¤ ¾ à ¦ , ¾ à ´���¢ ¾ ¬á± � ·1¦âÁ�¢É¶äãK± � ¤ » ·1¦The last two methods are efficiently (Batagelj, 1991, 1994) [4] implemented in Pajek
and can be applied also on (very) large acyclic networks. Let ª Ó ¢ ¥�¦ denotes the numberof different paths from � to
¥, and ª � ¢ ¥§¦ denotes the number of different paths from
¥to» . Then ª ¢ £Ò¤N¥�¦u� ª Ó ¢ £¦ Õ�ª � ¢ ¥�¦:¤�¢ £Ò¤N¥§¦Ü ¾ .ª and ªÖà are flows in the network since they obey the Kirchoff’s node law:
For every node¥
in a citation network¢É¶�¤ ¾ ¦ in standard form it holds
incoming flow�
outgoing flow
Therefore the total flow through the citation network equals ª ¢ » ¤ � ¦ . This gives us a naturalway to normalize the weights
Ï ¢ £Ò¤N¥�¦u� ª ¢ £Ò¤N¥�¦ª ¢ » ¤ � ¦ å æ�ç Ï ¢ £ ¤N¥§¦ ç²è
If é is a minimal cut-set it also holds êë�ì-í î:ïZð�ñ Ï ¢ £Ò¤N¥�¦�� è
We can assign weights also to vertices
Ï ¢ ¥�¦u�áª Ó ¢ ¥§¦ Õ�ª � ¢ ¥§¦ª ¢ » ¤ � ¦References
Layouts of graph A
In graph A the relation is the reverse of the citing relation. The original graph A has 311vertices. It has 6 weak components. Searching for strong components (testing acyclicity)it turns out that the graph A is not acyclic. A large strong component was generated byan erroneous arc ( GD94/143 Eades, GD98/423 Eades). After reversing it 4 small strongcomponents remained, corresponding to mutual references
±GD94/286 Garg, GD94/298
Papakostas·,±
GD94/328 Di Battista, GD94/340 Bose, GD94/352 ElGindy·,±
GD95/8Alt, GD95/234 Fekete
·and
±GD95/140 Chandramouli, GD95/300 Heath
·. To obtain
an acyclic graph, required by citations analysis method, we applied the following ’preprint’transformation:
58
Each paper from a strong component is duplicated with its ’preprint’ version. The papersinside strong component cite preprints.
The pictures were exported as nested partitions into SVG format that allows interactivedisplay of different slices – subgraphs induced by arcs with weights larger than a thresholdvalue. These pictures are available at
http://vlado.fmf.uni-lj.si/pub/GD/GD01.htm.In the paper form we can present only some snapshots.The first picture displays complete network after ’preprint’ transformations (320 ver-
tices). The vertices are put in layers (vertical position and color of vertices) according tothe years of publication. The placement of vertices inside the layer was determined by lo-cal optimization. The width and the color density of an arc and the size of a vertex areproportional to their citation weights.
The second and the third picture display the main parts (slices) of the citation networkat threshold values 0.02 and 0.05. The red arcs belong to the ’main path’.
59
Figure 46: Graph A – complete graph.
60
Figure 47: Graph A – level 0.02.
61
Figure 48: Graph A – level 0.05.
62
Graph B
To obtain the ’central symmetric’ picture of graph B energy drawing was used, followedby manual grid positioning of vertices. To save the space the lower part of the picture wasmanually mirrored across the vertical axis.
P0
T8+
P-2
2
P0
P-22
T8+P
+22
T9+
P-2
2
T9+
T9+
T8-
T8+
T9+
T9-
T8- T8+
T9+
T9-
T8-
T8+
T9-T9+
T8-
T9-
T9+
T0+
T9+
P-90
T9+ T8+
P-6
0
P+90
T9+
T8+T8+
T8+
+90 posturn right
turn right equalizer
0 pos turn left equalizer
+22 pos
turn left+22 - +90 intermediate
0 - +22 intermediate
turn right equalizer
-22 pos
turn right
-90 pos turn left
-60 pos
turn left equalizer
0 - -22 intermediate
-22 - -90 intermediate
Figure 49: Graph B – ’central symmetric’.
Graph C
Graph C is an acyclic directed graph. Such graphs can be topologically sorted. The corre-sponding adjacency matrix has zero lower triangle and diagonal. Since the graph is ratherdense we decided to use the matrix representation to visualize the graph structure. Layersare represented by blocks divided by blue lines.
63
P0
T8+
P-2
2P
0P
-22
T8+P
+22T9+
P-22
T9+
T9+
T8-
T8+
T9+
T9-
T8- T8+
T9+
T9-
T8-
T8+
T9-T9+
T8-
T9-
T9+
T0+
T9+
P-90
T9+
T8+ P-6
0
P+90
T9+
T8+T8+
T8+
+90 posturn right
turn right equalizer
0 posturn left equalizer
+22 pos
turn left+22 - +90 intermediate
0 - +22 intermediate
turn right equalizer
-22 pos
turn right
-90 posturn left
-60 pos
turn left equalizer
0 - -22 intermediate
-22 - -90 intermediate
Figure 50: Graph B – mirror.
64
Pajek - shadow [0.00,1.00]RGCLGNV1V2V3VPPIPV3AMDPMIPPOMTV4tV4VOTVIPLIPMSTFSTPIT7aFEFSTPpCIT46STPaAITOFC36TFTHERHC
RG
CLG
NV
1V
2V
3V
PP
IPV
3AM
DP
MIP
PO
MT
V4t
V4
VO
TV
IPLI
PM
ST
FST
PIT
7a FEF
STP
pC
IT46 S
TPa
AIT
OFC
36 TF TH ER
HC
Figure 51: Graph C – matrix representation.
REFERENCES 65
References
[1] Hummon N.P., Doreian P. (1989): Connectivity in a Citation Network: The Develop-ment of DNA Theory. Social Networks, 11 39-63.
[2] Hummon N.P., Doreian P. (1990): Computational Methods for Social Network Anal-ysis. Social Networks, 12 273-288.
[3] Hummon N.P., Doreian P., Freeman L.C. (1990): Analyzing the Structure of theCentrality-Productivity Literature Created Between 1948 and 1979. Knowledge: Cre-ation, Diffusion, Utilization, 11(4), 459-480.
[4] Batagelj V. (1991): An Efficient Algorithm for Citation Networks Analysis. Presentedat EASST’94, Budapest, Hungary, August 28-31, 1994. First presented at the Seminaron social networks. University of Pittsburgh, January 1991.
[5] Batagelj V., Doreian P., and Ferligoj A. (1992): An Optimizational Approach to Regu-lar Equivalence. Social Networks 14, 121-135.
[6] Brandenburg, F. J. (1996): Graph Drawing. Proceedings of Symposium on GraphDrawing, GD95, Passau, Germany, September 1995, Springer-Verlag, Lecture Notesin Computer Science, vol. 1027, 224-233.
[7] DiBattista, G. (1998): Graph Drawing. Proceedings of Symposium on Graph Draw-ing, GD97, Rome, Italy, September 1997, Springer-Verlag, Lecture Notes in ComputerScience, vol. 1353, 438-445.
[8] Kratochvil, J. (1999): Graph Drawing. Proceedings of Symposium on Graph Draw-ing, GD99, Stirin Castle, Czeck Republic. September 15-19, 1999. Springer-Verlag,Lecture Notes in Computer Science, vol. 1731, 400-409.
[9] Marks, J. (2001): Graph Drawing. Proceedings of the 8th Symposium on Graph Draw-ing, GD00, Colonial Williamsburg, USA. September 20-23, 2000. Springer-Verlag,Lecture Notes in Computer Science, vol. 1984, 410-418.
[10] North, S. (1997): Graph Drawing. Proceedings of Symposium on Graph Drawing,GD96, Berkeley, California, USA, September 1996, Springer-Verlag, Lecture Notesin Computer Science, vol. 1190, 129-138.