Principles of Social Network Analysis

Definition of Social Networks

• “A social network is a set of actors that may have relationships with one another”

(Hannemann, 2001)

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NODE: PeopleOrganizationsRoles/positions

TIE:RelationshipsCommunicationsResource-sharingShared properties

NETWORK:

“Social entity”(group of friends, community, organization)

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Social Network Analysis

•Networks can have few or many actors (nodes), and one or more kinds of relations (edges) between pairs of actors.”

•“Social network analysis is the study of social structure and its effects.”

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Representation of Social Networks

• Matrices

• Graphs

Ann Rob Sue NickAnn --- 1 0 0Rob 1 --- 1 0Sue 1 1 --- 1Nick 0 0 1 ---

Nick

Ann

Rob

Sue

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One way and or two way connections

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Clique: all the points have direct relationship

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Clique: all the points have direct relationship

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12

Bridge: a relationship which Connect two cliques

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13

Isolate

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Structure matters…

… for the flow of information / likelihood of collective actionA B

Structure matters…

…for the access that individual members have to information and opportunities

Social capital and health: who you are connected to, and who they are connected to, has implications for your access to resources and your well-being

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Describing network structure

Density = proportion of realized ties

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Describing network structure

Density = proportion of realized ties

Indicator of the speed and completeness of information flow

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Clique: density equal to one

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Strength of weak ties

C

B

D

E

F

G

A

B

C

D

E

F

G

Weak ties (A—E)can be a source of strength

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Which one is a cluster?

C

B

D

E

F

G

B

C

D

E

F

G

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Clustering coefficient: likelihood that any 2 nodes that are connected to the same node are connected

themselves.

C

B

D

E

F

G

B

C

D

E

F

G

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Clustering

• The degree to which decision making is done in collaborative groups.

• High rates of clustering are even more indicative of closed subgroups

• Clustering will inhibit spread between groups but accelerate it within groups

• Higher clustering will increase the importance of bridges that connect clusters

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Hierarchical structure

21

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• Centralization

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Examples of Dense Networks (Density=36.4%)

Decentralized (9.1%) Centralized (50.9%)

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Examples of Sparse Networks (Density=18.2%)

Decentralized (0.0%) Centralized (87.3%)

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27

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Centralization

• The centralization score is expressed as a percentage and can vary from 0 (every member is connected to every other member) to 100 (all members are connected to only 1 member).

• The centralization percentage thus indicates the degree of asymmetry in the distribution of connections in the network.

• A high centralization score indicates that some members have many more connections than others.

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Diffusion When Adopters Persuade Non-adopters at a Rate of One Percent

Time Cumulative Non-adopters RateNew Adopters

1 0.00 100.00 0.01

2 5.00 95.00 0.01 4.75

3 9.75 90.25 0.01 8.80

4 18.55 81.45 0.01 15.11

5 33.66 66.34 0.01 22.33

6 55.99 40.01 0.01 24.64

7 80.63 19.37 0.01 15.62

8 96.25 3.75 0.01 3.61

9 99.86 0.14 0.01 0.14

10 100.00 0.00 0.01 0.00

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Diffusion for Random Mixing

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Describing network structure

Centrality

“Betweenness”How often a node lies along the communication pathway between other nodes

E

B

D

C

B

E

C

D

A

A is a gatekeeper of information

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Describing network structure

Centrality

“Degree”Number of ties that a node has with others in the networkNode-level indicator of influence and prominence within the network A sends out 3 ties

and receives 2

E

B

C

D

A

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3321 33/40

3421 34/40

3521 35/40

• High indegree centralization would indicate that a small number of members are consulted by the rest of the members.

• High outdegree centralization would indicate that a small number of members do most of the consulting of others.

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1. Degree Centrality: The number of direct connections a node has. What really matters is

where those connections lead to and how they connect the otherwise unconnected.

2. Betweenness Centrality: A node with high betweenness has great influence over what flows in the

network indicating important links and single point of failure.

3. Closeness Centrality: The measure of closeness of a node which are close to everyone else. The

pattern of the direct and indirect ties allows the nodes any other node in the network more quickly than anyone else. They have the shortest paths to all others.

We measure Social Network in terms of:

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Basic Network Concepts

• Density: proportion of pairs of points connected bylines

• Clique: all the points have direct relationship

• Component: Points that directly or indirectly connect to each other

• Bridge: a relationship which Connect two cliques

• Dyad: bilateral relationship between two points

• Degree: number of connections of each network element with others

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Basic Network Concepts

• Homophily: Tendency to form relationships with socially similar others

• Transitivity: Tendency toward closure that results in clustering within a network

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1 2

8

9

7

6

5

4

3

10

12

11

2 Types of Network Data

1

2

Ego-Centric Sociometric

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