INTRODUCTION TO NETWORK ANALYSIS FOR …liberalarts.oregonstate.edu/sites/liberalarts.oregon... ·...

INTRODUCTION TO NETWORK

ANALYSIS FOR POLICY RESEARCH

Some Network Diagrams Provided with permission by James Moody, Duke University

and Lada Adamic, University of Michigan under Creative Commons License

Mark Lubell, UC Davis

Outline

What is network analysis?

Network science

Social science theoretical foundations

Network data collection

Three empirical case studies: water management,

sustainable viticulture, climate science

Network analysis workshop for ORA

“How behavior and institutions are affected by social relations is one of the classic

questions of social theory.”—Granovetter, 1985, The Problem of Embeddedness

“One of the most potent ideas in the social sciences is the notion that individuals are

embedded in thick webs of social relations and interactions…the problem of social

order: how autonomous individuals can combine to create enduring, functioning

societies.”—Borgatti et al. 2009, Science

Why Networks?

What is Network Analysis?

Social networks consist of a set of actors and the

relationships or ties between them

Social network analysis (SNA) quantifies the

properties of a network to understand how it

functions

SNA assumes that social structure matters in shaping

in individual behavior

Think Relationally

• Relation: A property of two or more entities

– Linkage – Tie

– Interaction

– Connection

– Relationship

– Association

– Involvement …

A

B

C D

E

Generality of a

relational perspective

16 Slide courtesy of Katherine Faust, UC Irvine

17

Elements of a Social Network

• Actors – social units

• Relations – ties between or among actors

A

B E

C D

Slide courtesy of Katherine Faust, UC Irvine

Graph and sociomatrix

A

B

C D

E

7

Actors

Act

ors

A B C D E A 1 B 1 1 1 C 1 1 1 D 1 E 1 1


Graph and sociomatrix

A

B

C D

E

8

Actors

Act

ors

A B C D E A - 0 1 0 0 B 0 - 1 1 1 C 1 1 - 0 1 D 0 1 0 - 0 E 0 1 1 0 -


Network Science

Computer science, physics, mathematics, social

sciences, natural sciences—a merger is occuring

Graph theory

Erdos-Renyi (Bernoulli) random graph

Barabasi-Albert Model of preferential attachment

Watts-Strogatz small-world networks

“scale-free” degree distributions

Network Science is a new journal for a new

discipline - one using the network paradigm,

focusing on actors and relational linkages, to inform

research, methodology, and applications from

many fields across the natural, social, engineering

and informational sciences.

Random Graph Models

Erdos Renyi

Barbasi Albert preferential attachment

Small World Networks

Theoretical Perspectives in Social

Science

Evolution of cooperation: reciprocity, multi-lateral relationships, long time horizon

Social capital: trust, reciprocity, and networks of civic engagement

Common pool resource management: Cooperation and local institutions needed to

overcome tragedy of commons and provide local public goods

Resilience: Capacity of social-ecological systems to bounce back after shock and

adapt to change; also important concept in network theory in physics and computer

science

Value chains: In a food system, the links between producers and consumers as food

moves through system—rightly viewed as “value networks”

Diffusion of innovation: Information of about innovations diffuses through social

networks

Communities of practice: Communities knit together to address common problems

and share knowledge about practices

Weak ties and structural holes: Closure versus search in networks

Policy Networks Framework

Scientific Consensus and Questions

Everybody thinks that networks matter, especially for

environmental policy

Density, reciprocity, and overall “social distance” seem to be

fairly well accepted

Less consensus on role of transitivity and clustering; probably

useful to have a some level of transitivity and clustering to

maintain local cooperation

Less consensus on bridging-bonding; you generally want to

increase bridging but system will be brittle without at least

some bonding

Optimal tradeoffs could depend heavily on context

16 16

Network Data Collection

Informant reports Questionnaire or interview

Systematic observation

Archival records

Experiment

Other Link trace

Small world

Diary

Sensors


17 17

Questionnaire / Interview

Roster vs. Free-recall (name generator)

List of population members or not

Fixed choice vs. free choice

Fixed number of nominations or not

Fixing number of nominations is generally a bad idea

Dichotomous or valued

Rating, ranking

Pros and cons …


18

Roster vs. free recall

Roster:

Below are the names of members of your work group. Which of them do you socialize with?

Ann

Bob

Carlos

Diana

Free recall (name generator):

Think of the members of your work group. Name the ones you socialize with.


19

Fixed vs. free choice

Fixed choice

Please indicate your

three closest friends.

Free choice

Please indicate the

people who you

consider to be friends.

You may name as

many or as few as you

wish.


20 20

Ties between people dichotomous, free

list

Asked of each person in the network

“Who would you go to for advice at work?”

“Who, at work, do consider your friends?”

Krackhardt high-tech managers network Slide courtesy of Katherine Faust, UC Irvine

21 21

Ties between people

valued, roster

Each person was asked to indicate for each other

person whether he/she:

0) did not know the other

1) had heard of the other but had not met him/her

2) had met the other

3) was a friend of the other

4) was a close personal friend of the other

Freeman et al. EIES network Slide courtesy of Katherine Faust, UC Irvine

Three Case Studies

Water management in an “ecology of games”

(Lubell, Robbins, Weng)

Sustainable Viticulture in California (Lubell,

Hoffman, Hillis)

Climate change networks (Lubell, Schwartz, Peters)

IRWM

Bay Area

Water

Forum

Bay Area Joint

Venture

Sonoma Creek

TMDL

Core Hypotheses

Institutions hypothesis: Collaborative institutions

designed for policy coordination are more central in

the network

Actor hypothesis: Actors with greater capacity have

more power in the network

“Risk” hypothesis (Berardo and Scholz 2010):

Network closure facilitates cooperation

Affiliation Network Analysis

Focuses on actors choosing to be in games

Exponential Random Graph Models: Compare observed frequencies of different “network” configurations to predictions from different “null” models

Key network processes: Activity (average degree), centralization(variance in degree), and closure (clustering)

Hypothesis tests:

Government agencies and collaborative institutions should have highest activity, most central, and most closure

Network closure structures more prevalent than expected from simple “random” process

The Bay Area Ecology of Games

Most Central Nodes

Centrality by Type (Species)

Table 2: ERGM Model Parameter Estimates

Naïve Actor Model

Political Capacity Model

Strategic Decision Model

Strategic Geography Model

General Parameters

Density -3.88 (0.03)* -3.75 (0.07)* -7.01 (0.35)* -5.77(0.36)*

Centralization (actors) --- --- 0.61 (0.11)* -0.21(0.11)

Centralization (institutions) --- --- 1.36 (0.18)* 0.56(0.18)*

Closure (actors) --- --- -0.19(0.05)* -0.06(0.04)

Geographic Centralization --- --- --- 1.57(0.05)*

Actor Type Activity Parameters (Local Government is Excluded Category)

Federal Government --- 0.45 (0.15)* 0.43 (0.16)* 1.82(0.18)*

State Government --- 0.19 (0.14) 0.16 (0.13) 1.35(0.16)*

Water Special District --- 0.13 (0.09) 0.12 (0.09) 0.42(0.10)*

Environmental Special District --- 0.29 (0.17) 0.26 (0.17) 0.46(0.19)*

Environmental Group --- -0.18 (0.10) -0.16 (0.09) -0.01(0.10)

Industry Group --- -0.59 (0.26)* -0.50 (0.23)* 0.05(0.29)

Education/Consulting --- -0.40 (0.18)* -0.32 (0.17) -0.06(0.19)

Actor Coalition --- -0.03 (0.34) -0.03 (0.33) 0.44(0.38)

Other Activity --- 0.07 (0.48) 0.11 (0.43) 1.33(0.54)*

Institution Type Activity Parameters(Collaborative Partnership is Excluded Category)

Interest Group Association Activity --- -0.22 (0.10)* -0.09 (0.09) -0.04(0.06)

Advisory Committee Activity --- -0.16 (0.12) -0.10 (0.11) -0.03(0.06)

Regulatory Process Activity --- -0.78 (0.16)* -0.61(0.15)* -0.36(0.12)*

Actor as Venue Activity --- -0.70 (0.19)* -0.47 (0.16)* -0.26(0.13)*

Joint Powers Authority Activity --- 0.16 (0.16) 0.15 (0.15) 0.06(0.10)

Note: Cell entries are ERGM parameter estimates with standard errors in parentheses. All models are estimated with “exogenous hubs”, with fixed degree distributions for nodes with greater than 20 edges. *Reject null hypothesis of parameter=0, p<.05.

Residual Analysis: Federal

Government Actors in Strategic

Geography Model

Table 3: Residual Analysis Showing T-Statistics Greater Than Two

Centralization Closure

Actor Types

Federal Government 4.7

State Government 2.0 4.2

Local Government 14.0

Water Special District 4.8 25.9

Environmental Special District

Environmental Group 6.9

Industry Group

Education/Consulting

Actor Coalition

Other Activity

Institution Types

Interest Group Association 17.5

Collaborative Partnership 8.9

Advisory Committee

Regulatory Process

Actor as Venue

Joint Powers Authority

SOCIAL NETWORKS AND DECISION-MAKING

IN SUSTAINABLE AGRICULTURE:

INNOVATION OR COOPERATION?

Mark Lubell, Matthew Hoffman, Vicken Hillis

Sustainable Viticulture

Partnerships in California

Integrated Pest Management

Self Assessment Workbooks

Third-party Certification

Statewide Program

http://www.lodiwine.com/lodirules_farming_standards1.shtml

http://www.vineyardteam.org/

Sustainability Partnerships:

Lodi, Central Coast, Napa

Social Networks: Information

and Cooperation

Sustainable Practice

Adoption: Individual and

Social Benefits

Question 2: Restructuring

Social Networks

Question 1: Diffusion or

Cooperation

Question 3: Participation

Increases Adoption Rate

Conceptual Framework

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%"Very useful" "Never used"

0% 10% 20% 30% 40% 50% 60% 70%

Published material

Organizations

Personal relationships

Personal experience

Lodi Grower

Knowledge

Network

n=46

n=25

n=140

0.00

0.05

0.10

0.15

0.20

0.25

Both Outreach Grower

n=1

n=32 n=9 n=10 n=3 n=13 n=8

0.00

0.20

0.40

0.60

0.80

1.00

1.20

Average

Centrality by

Type

Average Centrality of

Outreach Professions

Napa

Valley

Network

Vic

ken

Hillis, D

isse

rta

tion

Ana

lysi

s

Traditional Extension Model

University Scientist

County Advisor

Farmer

Carr, Anna, and Roger Wilkinson. 2005. "Beyond Participation:

Boundary Organizations as a New Space for Farmers and Scientists to

Interact." Society & Natural Resources 18 (3): 255-265.

“For many years agricultural

science assumed that research

was done by scientists,

repackaged by extension

officers, and launched at

farmers. Both their knowledge

systems and cultural roles were

seen as different. Nowadays

their roles are converging and

their boundaries are eroding.”--

Extension 3.0 as a Knowledge Network

Climate Science Networks and Public Lands

(with Mark Schwartz and Casey Peters)

Public lands management must adapt to climate change

National programs are pushing local land management

units in various ways, with national-level coordination

DOI Landscape Conservation Cooperatives

Science network programs created by USGS (Climate

Science Centers) and NOAA (RISAS)

Intermountain West Region of NPS

Figure 2. Management Consequences of Physical Climate Change Impacts

Figure 3. Management Consequences of Biological Climate Change Impacts

Conclusion: Networks Matter!

Networks mediate between institutions and individual behavior

Crucial for cooperation and innovation/learning in environmental policy

Decent tools available for studying structure of networks

Important frontiers: longitudinal, comparative, dealing with missing data, mathematical models, network management, connecting with outcomes

Network Analysis Definitions

•Nodes/Actors

•Edge/Ties/Relationship

•Binary/Dichotomous Network

•Valued Network

•Graphs/Networks

•Adjacency Matrix

•Directed Network

•Undirected Network

•Sociogram/Network diagram

•Attributes

Receiver 1 (AED)

Receiver 2 (USAID)

Receiver 3 (NGO)

Sender 1 (AED) Diagonal; self reference

0 1

Sender 2 (USAID)

1 Diagonal; self reference

0

Sender 3 (NGO)

1 1 Diagonal; self reference

Gettin

g D

ata

Int

o O

RA

Procedure: FileData Import WizardTable Data from Excel or text Rectangle of link weights Click through “next” buttons entering required infoEnter filename with “agent to agent” designation

Ad

d A

ttrib

utes

Procedure: Select “Agent” nodeSelect “Editor” tabClick Attributes “Import” Select “file” to importMake sure the first column in attribute file has same labels as network rows; ORA uses them as an index (I think)

Manage Data

Choices depend on application

Remove isolates (for example, if you have missing

survey data)

Binarize (if valued data don’t add info)

Symmetrize (if directional data doesn’t matter)

Procedure: Select “Data Management” menuSelect “Metanetwork transform”Select appropriate check boxes

Netw

ork

Vis

ualiz

ation

Procedure: Select “AgentXAgent” nodeClick Visualize this NetworkPlay with all kinds of things (Color nodes by attribute, size nodes by centrality, eliminate isolates)

Descriptive Statistics for Networks

Just like descriptive stats for ordinary, rectangular

data

Network level stats

Node level stats

Community Detection

Statistical models (not covered here)

Network Density

Density: Number of ties present divided by

maximum

For example, out of 12

possible connections, this graph

has 7, giving it a density of

7/12 = 0.583

Click to highlight your metanetwork( however named) Generate ReportsStandard Network Analysis Click through options to the end

Procedure

Reciprocity

Ratio of number of edges that are reciprocated over total number of relations in a network

In this example, there are 1/3 are reciprocal


Procedure

Average Path Length

The length of a path between two nodes is a count of the number edges that connects them. The distance between two nodes is the shortest path.

Average distance is the average of the shortest path for all pairs of nodes

In example, there is one path from blue to green of length 2 (shortest path) and another of length 3

Average distance for a node is the average of the shortest path lengths to all other nodes

Average (or characteristic) path length is the average of the average distance for the nodes


Procedure

Local and Global Clustering

The local clustering coefficient calculates the average density of ties between nodes directly adjacent (local neighborhood) to a focal node (ego), excluding the ties to the node itself

In the example, the blue node is the ego and red nodes are the local neighborhood. Density of ties (blue arrows) in local neighborhood is 2/6; cohesion averages this score overall all ties

Global clustering (UCINET cohesion): Average of the local clustering

High clustering relative to density is linked to sub group formation


Procedure

Network Transitivity

Three nodes (a triple) i,j,k are transitive if whenever node i is connected to node j and j is connected to k then vertex i is connected to vertex k.

The density of transitive triples is the number of triples which are transitive divided by the number of paths of length 2, i.e. the number of triples which have the potential to be transitive.

A triple is transitive if:

If iJ and Jk, then

ik

i k

J

i k

J

Valued Networks (note possible bug in

UCINET as of November 10, 2010 but they claim it was fixed)

Binary Networks

Procedure NetworkCohesionTransitivitySelect "Strong" Enter your "Filename"

NetworkCohesionTransitivitySelect "Adjacency" Enter your "Filename"

Output Transitivity: % of ordered triples in which i-->j and j-->k that are transitive

Transitivity: % of ordered triples in which i-->j and j-->k that are transitive

Network Centrality

In a directed graph, the in-degree of a node is the number of ties received by that node and the out-degree is the number of ties initiated by that node.

Blue node in example: In-degree=3, and out-degree=2.

Normalized degree is score relative to maximum that could be obtained

“Network” centralization is how centralized the observed network is relative to the most centralized possible, the “star” network

Valued Networks Binary Networks

Procedur

e Procedure: NetworkCentralityDegree Select "No" for all choices Enter your "Filename"

Procedure: NetworkCentralityDegree Select "No" for all choices Enter your "Filename"

Output In Degree and Out Degree (do not use normalized for valued networks)

NrmInDegree, NrmOutDegree, Network Centralization (Outdegree), Network Centralization (Indegree)

Centrality-Betweenness


Procedure NA Procedure: NetworkCentralityFreeman Betweenness Node Betweenness Enter your "Filename"

Output NA nBetweenness, Network Centralization Index

A B C E D A lies between no two other vertices

B lies between A and 3 other vertices: C, D, and E

C lies between 4 pairs of vertices (A,D),(A,E),(B,D),(B,E)

A particular node is “between” another pair if it sits on the shortest path between the other pair

For each node, betweenness is a sum of the fraction of shortest paths between other pairs on which that node sits

Normalized betweenness is relative to the maximum that could be obtained

“Network” centralization is how centralized the observed network is relative to the most centralized possible, the “star” network

External-Internal (E-I) Index

Valued Networks Binary Networks Procedure Procedure: NetworkCohesionE-I

IndexEnter Your Attribute "Filename" Enter your Network Filename "Filename"

Procedure: NetworkCohesionE-I IndexEnter Your Attribute "Filename" Enter your Network Filename "Filename"

Output Re-scaled E-I Index, smallest value of p-values in permutation test table, group-level E-I indexes for each stakeholder group

Re-scaled E-I Index, smallest value of p-values, in permutation test table group-level E-I indexes for each stakeholder group

The E-I index provides a measure of the relative number of relationships within a

group (bridging), versus out-group ties that cross group boundaries (bonding).

The E-I index calculates the number of out-group ties, subtracts the number of in-

group ties, and then divides by the total number of ties in the network.

For example, if there are 20 ties in the whole network and 2 groups with all in-group

ties, the E-I index would be [0 (out-group)-20 (in-group)/20]=-1. If all ties were out-

group, then the E-I index would be [20 (out-group)-2 (in-group)/20]= +1. The E-I

index thus ranges between -1 and 1, and directions of ties are ignored.

Ego Networks


Procedure N/A Procedure: NetworkEgonetEgonet Basic Measures Select "Undirected"Enter your Network Filename "Filename"

Output N/A Size, Ties, Density, and nBetweeneness for all nodes

Ego-networks are the local neighborhood of a

particular node; for example the blue node in the

diagram

Ego-networks are good for participatory planning or

isolating a particular organization for some contextual

reason

Ego-network analysis in UCINET looks at the binary

networks, and calculates a variety of relevant stats for

each ego-network

Visualization of Ego-Networks is done from NetDraw

Advanced Topics

Structural holes

Group detection algorithms, e.g., cliques, Newman-

Girvan, multidimensional scaling, structural

equivalence

QAP correlation and regression

Exponential random graph and other statistical

models

Software

UCINET—most basic and user friendly

R, statnet and other packages

ORA—newer program, very nice graphics, lots of

interesting descriptive stats

PAJEK—large networks, heavily used

MELNET, statistical models

SIENA, actor-oriented models, ERGM (but now in R)

Many others…

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