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Introduction to Network Science and Complex Systems
March 23, 2018
Rosen College of Hospitality Management
University of Central Florida
Jalayer (Jolly) Khalilzadeh, Ph.D. Candidate
CONTENT Bibliography: Network Footprint
Origins and History
Definitions and Terminology
Complexity & Complex Systems
Network Models
Conceptual Structure
Future: Potential Areas
Resources
BIBLIOGRAPHY: NETWORK FOOTPRINTArticles 175
Sources (Journals, Books, etc.) 51
Period 1985 - 2018
Average citations per article 21.93
Authors 326
Authors per Article 1.86
Year Articles2018 72017 342016 152015 172014 92013 142012 92011 172010 122009 62008 102007 42006 62005 42004 22003 12002 12001 12000 21999 11998 11997 11985 1
Growth: 9.25
BIBLIOGRAPHY: NETWORK FOOTPRINT
Source Articles
Tourism Management 21
Annals of Tourism Research 17
Current Issues in Tourism 10
Tourism Review 9
Asia Pacific Journal of Tourism Research 7
International Journal of Contemporary Hospitality Management 7
International Journal of Hospitality Management 7
Tourism Analysis 6
Tourism Geographies 6
International Journal of Tourism Research 5
(Mathematical Association of America (MAA), Euler Archive, 2018)
ORIGIN: SEVEN BRIDGES OF KÖNIGSBERG
Leonhard Euler1707-1783
ORIGIN: SEVEN BRIDGES OF KÖNIGSBERG
ORIGIN: SEVEN BRIDGES OF KÖNIGSBERG
a b c d e f
a 0 1 0 0 0 0
b 0 1 0 0 0 0
c 1 0 0 0 0 0
d 1 1 1 0 0 0
e 0 0 85 1 0 0
f 0 0 0 1 1 0
DEFINITIONS &TERMINOLOGY
Vertex, Node, Actor,Ego/Alter
Edge, Link, Arc
a
b
c
d
e
f
A B C D
A 0 1 1 1
B 1 0 0 1
C 1 0 0 1
D 1 1 1 0
85
= 1
= 2
= 3=
3
= 2 or 86 ?
a b c d e f g h i j
A 1 0 1 1 0 0 0 0 0 0
B 1 1 0 0 0 1 1 0 0 1
C 1 1 0 0 0 0 0 0 1 0
D 0 0 0 0 1 0 0 1 0 0
DEFINITIONS &TERMINOLOGY
a
A
B
C
bc
df
g
i
j
D
e
h
𝐌×𝐌𝐓
Porter, M. A. (2018)
COMPLEXITY & COMPLEX SYSTEMSDefinition
o System
o Components (large number)
o Interaction
o Difficulty of behavior modeling
o Nonlinearity
o Spontaneous order
o Adaptation
o Feedback loops
Exampleso Brain
o Body
o Ecosystem
o City
o Economy
o Climate
Complex
Simple
Complicated
Chaos
NETWORK MODELS
Random Scale-Free Small-World ERGMs Dynamic
NETWORK MODELS
Random Scale-Free Small-World ERGMs Dynamic
Measures:
•Order (N): 400
•Size (E): 747
•Transitivity: 0.0074
•Average Distance: 4.6
•Density: 0.0094
•Mean Degree: 3.735
•Components: 11
NETWORK MODELS
Random Scale-Free Small-World ERGMs Dynamic
Measures:
•Order (N): 400
•Size (E): 399
•Transitivity: 0
•Average Distance: 7.32
•Density: 0.005
•Mean Degree: 1.995
•Components: 1
NETWORK MODELS
Random Scale-Free Small-World ERGMs Dynamic
Measures:
•Order (N): 400
•Size (E): 2800
•Transitivity: 0.55
•Average Distance: 3.34
•Density: 0.035
•Mean Degree: 14
•Components: 1
o Random Rewiring
COMPARATIVE ATTRIBUTESDistribution
Barabási, A. L., & Frangos, J. (2014)
Generative Networks
Generative Models PA Functions Fitness ReferenceGT model Free Free Pham et al.
Callaway et al. Ak = 1 ηi = 1 Callaway et al.
BA model Ak = k ηi = 1 Barabási and Albert
Extended BA model Ak = kα ηi = 1 Krapivsky et al.
Krapivsky et al. Free ηi = 1 Krapivsky et al.
Caldarelli model Ak = 1 Free Caldarelli et al.
BB model Ak = k Free Bianconi and Barabási
Extended BB model Ak = kα Free Not previously considered.
o Preferential attachment (PA) aka rich-get-richer
o Fitness aka fit-get-richer
COMPARATIVE ATTRIBUTES
Pham, T., Sheridan, P., & Shimodaira, H. (2016)
Simulation
Attack & Random Errors
COMPARATIVE ATTRIBUTES
o Percolation
• Site percolation• Bond percolation
Albert, R., Jeong, H., & Barabási, A. L. (2000)
3D Representation
⇝
COMPARATIVE ATTRIBUTESControlling the Network
𝑃 𝑥 = C𝑥−𝛾 , for x ≥ 𝑥𝑚𝑖𝑛
Liu, Y. Y., Slotine, J. J., & Barabási, A. L. (2011)
Type Name Order (N) Size (E) nDRegulatory TRN-Yeast-1 4,441 12,873 96.5%
Regulatory Ownership-USCorp 7,253 6,726 82.0%
World Wide Web nd.edu 325,729 1,497,134 67.7%
Trust WikiVote 7,115 103,689 66.6%
Internet p2p Gnutella 10,876 39,994 55.2%
Social communication Email-epoch 3,188 39,256 42.6%
Power grid Texas 4,889 5,855 32.5%
Food web Seagrass 49 226 26.5%
Electronic circuits s838 512 819 23.2%
Citation ArXiv-HepTh 27,770 352,807 21.6%
Social communication Cellphone 36,595 91,826 20.4%
Trust College student 32 96 18.8%
Neuronal Network Caenorhabditis elegans 297 2,345 16.5%
Trust Prison inmate 67 182 13.4%
Intra-organizational Consulting 46 879 4.3%
Intra-organizational Manufacturing 77 2,228 1.3%nD: Nodes (driver nodes) involved in the control process
⇝
COMPARATIVE ATTRIBUTESControlling the Network
𝑃 𝑥 = C𝑥−𝛾 , for x ≥ 𝑥𝑚𝑖𝑛
Liu, Y. Y., Slotine, J. J., & Barabási, A. L. (2011)
NETWORK MODELS
Random Scale-Free Small-World ERGMs Dynamic
Global Model
Local Model
NETWORK MODELS
Random Scale-Free Small-World ERGMs Dynamic
Susceptible-Infected(SI)
Susceptible-Infected-Recovered/Removed (SIR)
Susceptible-Infected-Recovered-Susceptible (SIRS)
Simulation
Newman, M. (2010)
CONCEPTUAL STRUCTUREKey Words Articles
NETWORK ANALYSIS 70
TOURISM 33
SOCIAL NETWORKS 27
SOCIAL NETWORK ANALYSIS 24
TOURISM MANAGEMENT 24
ACTOR NETWORK THEORY 18
NETWORK 15
TOURISM DEVELOPMENT 15
TOURIST DESTINATION 14
STAKEHOLDER 13
DESTINATION MANAGEMENT 11
TOURISM MARKET 10
SOCIAL CAPITAL 9
CHINA 7
INNOVATION 6
Castellani, B. (2018)
FUTURE: POTENTIAL AREAS
RESOURCESReference Books
o Newman, M. (2010). Networks: an introduction. Oxford university press.o Barabási, A. L. (2016). Network science. Cambridge university press.o Jackson, M. O. (2010). Social and economic networks. Princeton university press.o Scott, J., & Carrington, P. J. (2011). The SAGE handbook of social network analysis. SAGE publications.o Barabási, A. L., & Frangos, J. (2014). Linked: the new science of networks science of networks. Basic Books.o Watts, D. J. (2004). Six degrees: The science of a connected age. WW Norton & Company.o Christakis, N. A., & Fowler, J. H. (2009). Connected: The surprising power of our social networks and how they shape our
lives. Little, Brown.o Rainie, L., & Wellman, B. (2012). Networked: The new social operating system. Mit Press.o Barabási, A. L., & Gelman, A. (2010). Bursts: The hidden pattern behind everything we do. Physics Today, 63(5), 46.o Alhajj, R., & Rokne, J. (2014). Encyclopedia of social network analysis and mining. Springer Publishing Company,
Incorporated.o Barnett, G. A. (2011). Encyclopedia of social networks (Vol. 1). Sage.o Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications (Vol. 8). Cambridge university
press.o Scott, N., Baggio, R., & Cooper, C. (2008). Network analysis and tourism: From theory to practice. Channel View
Publications.
RESOURCES
Instruction Books
o Luke, D. A. (2015). A user's guide to network analysis in R. London, England: Springer.o Harris, J. K. (2013). An introduction to exponential random graph modeling (Vol. 173). Sage Publications.o Nagarajan, R., Scutari, M., & Lèbre, S. (2013). Bayesian networks in R. Springer, 122, 125-127.o Kolaczyk, E. D., & Csárdi, G. (2014). Statistical analysis of network data with R (Vol. 65). New York: Springer.o De Nooy, W., Mrvar, A., & Batagelj, V. (2011). Exploratory social network analysis with Pajek (Vol. 27).
Cambridge University Press.
RESOURCESSoftware Packages
o Pajek (http://mrvar.fdv.uni-lj.si/pajek/) o Gephi (https://gephi.org/)o Statnet
• ergm• tergm• network• sna• tsna• degreenet• latentnet• networksis• networkDynamic• relevent• EpiModel
o igrapho netdiffuseRo Bergmo Rsienao btergmo Hergmo GERGMo PAFito ndtv
o https://github.com/briatte/awesome-network-analysis
http://mrvar.fdv.uni-lj.si/pajek/https://gephi.org/https://github.com/briatte/awesome-network-analysis
Thank You