Social Network Analysis:What it Is, How it Works, and

How You Can Do It

Prof. Paul Beckman

San Francisco State University

Agenda

“Social networks” SNA: Social network analysis The math behind SNA My contribution to SNA research My SNA research SNA software Large dataset research example

Commercially,What Are Social Networks?

Theoretically,What Are Social Networks?

Groups of individuals who are often humans

but not necessarily: gorillas, dolphins, birds, etc. who “interact” in some setting

creating “links” between the individuals With humans, the setting is often professional

for example, in the workplace and NOT necessarily social

because social interactions are often hard to record without some computerized programmatic process such

as used by the firms on the previous slide

Social Network Analysis

SNA: research about/using social networks Other criteria are often needed

Frequently the “interaction” relates to a task For my research purposes:

group of individuals must be precisely defined task must be standardized task must have quantifiable performance

measurements task must be completed many times sub-groups must form, break up, and re-form in

different configurations to complete the task

The Math Behind SNA In math, SNA is call “graph theory”

one branch of mathematics Graph theory is the study of groups of

“nodes” points in a network

“edges” links between points in a network

It is also the study of: measures of node interaction

things you can say about an individual node measures of network structure

things you can say about the network as a whole

Other Graph Theory Terms

Edge weight Did two nodes get linked just once or were they

linked more than once? Did you just meet me or are you currently in ISYS 464?

Directed vs. non-directed graphs Is an edge from one node to the other or is the

edge non-directional? Example: at a party, you may:

know about someone: directional shake hands: non-directional

Example: “recommendation networks”: each node recommends other nodes and can be recommended

Example:Measuring “Degrees of Separation”

Firm #

Board Members

1 A, D

2 B, C

3 A, C

4 C, D, E

5 F,G

B

A

C

D

E

A B C D E

A 2 1 1 2

B 2 1 2 2

C 1 1 1 1

D 1 2 1 1

E 2 2 1 1

x 1.50 1.75 1.00 1.25 1.50

F

= board member

G1

2

Graphwith 2islands

Calculating connectivity 1. for each node: calculate the

shortest path to each other node

2. for each node: calculate mean of all shortest paths for that node

Other Connectivity Measures

In graph theory, we say “centrality” instead of “connectivity”

There are four common measures of centrality Degree centrality

simply: sum of other directly connected nodes Betweenness centrality

a more complex measure of “degrees of separation” Closeness centrality

average of all “degrees of separation” for a node Eigenvector centrality

measures “importance” of a node (Google’s PageRank)

My Contribution to SNA Research

Move beyond simply measuring network centrality or other graph-theoretic constructs and measures

Because: which is important in the real world? Who is most connected?

or How does connectivity relate to real-world task

performance?

My Contribution Requires . . .

Addition of a standard task because the real world cares about task

performance, NOT connectivity values but most SNA research focuses strictly on

information flow through the network and who is “important” in network information flow

Task has quantifiable performance measures so we can relate (in a mathematical way) network

measures to performance measures

My SNA Research

MIS researchers Kevin Bacon, Degrees-of-Separation, and MIS Res

earch VC board members

Do a Firm’s Board Member Linkages Relate to Perceived or Actual Firm Financial Performance?

Baseball players More Highly-Connected Baseball Players Have

Better Offensive Performance

SNA Software

Powerful (and complex) tools: UCINET

For very complex network calculations Pajek

For very large datasets Netdraw

For visualizing networks Weaker (and more simple) tools:

NodeXL

SNA Software: NodeXL

Easy-to-use tool http://nodexl.codeplex.com/

Runs inside Microsoft Excel as a template

NodeXL Example:Using Our Previous Dataset

Firm #

Board Members

1 A, D

2 B, C

3 A, C

4 C, D, E

5 F,G

B

A

C

D

E

A B C D E

A 2 1 1 2

B 2 1 2 2

C 1 1 1 1

D 1 2 1 1

E 2 2 1 1

x 1.50 1.75 1.00 1.25 1.50

F

= board member

G1

2

Graphwith 2islands

Calculating connectivity 1. for each node: calculate the

shortest path to each other node

2. for each node: calculate mean of all shortest paths for that node

NodeXL Centrality Calculations

We need data in “edgelist” format a standard format for entering data into SNA tools this is sometimes a tricky transformation

Node1 Node2

A C

A D

B C

C D

C E

D E

Large Dataset Example

U.S. professional baseball Players are nodes Links occur when players play together

as measured from team rosters

My Five Research Criteria

1. Precisely defined group of nodes? Yes: you are either a MLB player or not

2. Nodes interact in precisely quantifiable sub-groups? Yes: team rosters are defined by specific rules

3. Standard task that sub-groups perform? Yes: a baseball game has a specific set of (exact) rules

4. Task has quantifiable performance measures? Yes: both for players (BA, RBIs, etc.) and teams (wins,

runs, etc.)5. Sub-groups break up, re-form, and re-do the task

again? Yes: rosters change from day to day and year to year

Research Methodology

1. Get the dataset available online

2. Calculate centrality for each NON-pitcher over some time period

Why non-pitchers?

3. Calculate task performance batting average, home runs, RBIs, slugging pct.

4. Calculate correlation between centrality and individual performance

Correlation Calculation

Correlations between centrality measures and individual performance measures

“Correlation” varies from -1.00 to +1.00 example: list 1000 players by height vs. home runs

exactly the same order? correlation = +1.00 exact inverse order? correlation = -1.00

Results

BA = batting average HR = home runs hit RBI = runs batted in SLG = slugging percentage FPCT = fielding percentage

Degree Betweenness Closeness EigenvectorBA 0.30 0.20 0.34 0.26HR 0.48 0.46 0.39 0.42RBI 0.47 0.47 0.38 0.38SLG 0.37 0.25 0.37 0.35FPCT 0.04 0.03 0.07 0.05

Conclusions

Players with higher centrality have higher individual OFFENSIVE performance

measures but not defensive performance measures

This does NOT mean higher centrality leads to higher performance only that they are correlated

Limitations

Simplistic measure of a “link” opening day roster

misses subsequent changes in player connection Further simplistic measure of a “link”

binary, not weighted, links misses players who play together over a long time

Only measured correlation not causality

don’t know if one causes the other or perhaps are both caused by some other factor (age, experience, etc.)

So, Today We’ve Talked About:

What social networks are The math behind social networks

graph theory A free social network analysis tool you can use

NodeXL One particular large SNA research project

connectivity vs. performance of MLB players

Questions?