Social Network Analysis and Its

ApplicationsBy Paul Rossman

Indiana University of Pennsylvania

What is Social Network Analysis?

• The mapping and measuring of relationships and flows between people, groups, organizations, computers, web sites, and other information/knowledge processing entities.

Who uses it?• The following fields:

– Sociometry & psychometry• Jacob Moreno (sociogram)

– Social anthropology• kinship algebra

– Sociology• Durkheim

• SNA derives many of its concepts from discrete math from fields such as graph theory, group theory and matrix algebra.

Why Social Network Analysis?

• SNA violates traditional statistical tests– Assumes dependence rather than

independence – Need somehow to measure how “connected”

a group is or who the major players are in a network.

– Graph theory, and properties of matrices help us with this problem

Basics of graph theory

• A graph G(V,E) consists of …–Set of nodes | vertices V

representing actors–Set of lines | edges E

representing ties

•An edge is an unordered pair of nodes {u,v}

•Nodes u and v adjacent if {u,v} is an element of E– So E is subset of set of all

pairs of nodes

a b

c

d

e fa b

c

d

e fa b

c

d

e f

Directed Graphs (digraphs)

• Digraph D(V,E) consists of …–Set of nodes V

–Set directed arcs E

•An arc is an ordered pair of nodes {u,v}

•{u,v} is an element of E indicates u sends arc to v

•{u,v} is an element of E does not imply that {v,u} is an element of E

Graphs in SNA

• Directed graphs– Gave money to

• Undirected graphs– Attending meetings with– Friends with– Related to

Valued Graphs (vigraphs)

• Graphs can also be valued or non-valued.

• A valued graph has

numbers attached to the lines that indicate the strength or frequency or intensity or quantity of the tie between nodes.

Other Key Terms

• Adjacency Matrix: A binary nn matrix A in which aij = 1 and aji = 1 if vertex vi is adjacent to vertex vj, and

aij = 0 and aji = 0 otherwise.

USA Mexico UK Canada AlgeriaUSA 1 3 10 60 0Mexico 3 1 0 0 0UK 10 0 1 0 1Canada 60 0 0 1 2Algeria 0 0 1 2 1

Other Key Terms

• Degree: The degree da of vertex a is the number of vertices to which a is linked by an edge.

– The minimum possible degree is 0

– The maximum possible degree is n-1

Other Key Terms

• Centrality: Simply counting the in-ties and out-ties for each node

• Those which have the most are said to be the most influential in the network.

Centrality

• Degree: Number of ties to others. Row or column sums of adjacency matrix. – In a friendship network, degree may translate

to gregariousness or popularity

• Closeness: The graph-theoretic distance of a given node to all other nodes. – Simple closeness is an inverse measure of

centrality (Larger the numbers, the more distant the actor is)

Centrality

• Betweenness:– The number of "times" that any node needs a

given node to reach any node by the shortest path.

• Interpreted as indicating power and access to diversity of what flows; potential for synthesizing.

• Eigenvector: – Principal eigenvector of the (possibly valued)

adjacency matrix of a network. • Indicator of popularity, “in the know”• Tends to identify centers of large cliques

Applications

• Kevin Bacon Gamehttp://oracleofbacon.org/

• Baseball Oracle

• Erdos Number

So why did I learn this?

• Journalists have begun to use SNA to investigate relationships among officials and to visualize where money is going.

• It is a part of the field called computer-assisted reporting (CAR).

How are journalists using SNA?

• SNA has only been widespread for about 5 years in the mass media

• Journalists are using SNA to analyze:– Power in local government– Campaign contributions– Crime trends– Public health– Contracts and bids

SNA and public records• Sources for doing a social network analysis is

everywhere in public records– Local government Web sites– Form 990s– FEC Contributions– Property Records– Court Records

Good examples of SNA in Journalism

• In 2004, The Kansas City Star used social network analysis software to visualize U.S. government allegations that the Islamic African Relief Agency (IARA) in Columbia, Mo., helped finance bin Laden and other terrorists.

• In 2004, the Washington Post used it to look at the campaign fundraising practices of President George W. Bush’s main contributors.

John Kerry’s contributions

• The Washington Post also used it to analyze Kerry’s donors in the 2004 election.

John Kerry’s contributions

John Kerry’s contributions

John Kerry’s contributions

John Kerry’s contributions

Software

So how did I do this?

* Grin

-- http://www.geocities.com/pechv_ru/

* UCINET

-- http://www.analytictech.com/

Questions?

Presentation will be up at

http://www.paulrossman.net/presentations .html

Indiana County Data Center

http://www.indianagazette.com/datacenter