Network Theory and Analysis: A Primer Kun Huang, Ph.D. RWJF Center for Health Policy School of Public Administration

What is a Network? a set of actors or nodes along with a set of ties of a specified type (such as friendship) that link them. The ties interconnect to form paths that link nodes not directly tied. The pattern of ties yields the network structure. Source: Borgatti, S.P. Halgin, D.S On network theory. Organization Science, 1-14.

Ecological Networks

The World Financial Network

Dark Networks

Typical Relationships Source: Borgatti, S.P. et al “Network Analysis in the Social Sciences.” Science. 323 (5916). Feb 13,

Definition of Network Analysis Considers the whole network structure. Makes argument about how network structure influences individual action. Uses graphic displays Uses mathematical formalism. Source: Freeman, L. (2004).

Network Analysis: Historical Origins. 2000s -Network science (multidisciplinary). 1990s – UCINET IV released. – Wasserman & Faust (1994) textbook. 1970s– Rise of Sociologists. – Milgram small-world (late 60s) – White: block modeling (late 60s). – Granovetter’s weak ties (1973, 1974). – Freeman: measures of centrality (1979). 1960s (Cartwright & Harary) – Application of graph theory to sociogram. – Triads 1920s and 1930s (Lewin, Heider, & Moreno). – Field theory in physics – Hawthorne studies and use of sociogram.

Network Perspective Individuals are embedded in web of relations. – People’s health status is connected. Unit of analysis: dyad, triad, whole-network Interrelationship between embeddedness, individual attributes & individual outcomes.

Non-Network vs. Network Perspective Non-network perspective Individuals are atomistic Individuals are bundles of attributes (age, class, party affiliation) which cause behavior Research measures individual attributes & outcomes and correlates them Network Perspective Individuals embedded in thick web of relations, and have direct influence on each other Unit of data is the dyad – pairs of individuals Measures the pattern of relationships an individual is involved in and link that with outcomes.

Causality and Network Research Antecedents: psychology. Network variables: math, sociology, Consequences: management, sociology, public health. Network VariablesAntecedentsConsequences

An Example: Obesity Clusters Source: Christakis, N.A. and Fowler, J.D The spread of obesity in a large social network over 32 years. New England Journal of Medicine, 357(4): Circles with red borders = women, and circles with blue borders = men. The size of each circle is proportional to the person’s body-mass index. The interior color of the circles indicates the person’s obesity status: yellow = an obese person (body-mass index, ≥30) and green = a nonobese person. The colors of the ties between the nodes indicate the relationship between them: purple =a friendship or marital tie and orange= a familial tie.

Network Theories Strength of weak ties (Granovetter, 1974) Social capital (Saxenian, 1990; Burt, 2000). bonding and bridging ties. Network governance and effectiveness (Provan and Kennis, 2008; Provan and Milward, 2005). Network change/evolution(Koka and Prescott, 2006; Ahuja, Soda and Zaheer, 2012).

Conceptualizing Network Change Source: Koka, Madhavan and Prescott, The evolution of interfirm networks. Academy of Management Review, 31(3),

Key Structural Concepts Individual level – Measures of centrality Dyad level – Multiplexity Group-level – Cliques. Network-level – Density and centralization.

Degree Centrality Number of other actors with direct ties to ego. Directional vs. non-directional network. in-degree centrality and out-degree centrality.

Multiplexity The extent to which two actors are connected by more than one type of relationship. A measure of strength of ties (Monge & Contractor, 2003). Uniplex vs. multiplex ties.

Clique as Sub-structures of Networks A subset of networks in which the actors must be directly connected to each other and all the actors must have no direct common link to any other actors. (Kilduff & Tsai, 2003; Wasserman & Faust, 1994).

Density Ratio of number of linkages actually in place between network members by the number of potential linkages (Diani, 2002; Wasserman & Faust, 1994) L and g are the number of lines actually present in a network and the number of nodes in the network, respectively.

Network Centralization

CA(ni) and CA(n*) are an actor centrality index and the largest value of the particular index that occurs across the g actors in the network, respectively

Data Collection Methods Direct Observation Written Records – Examples include: intercampus mail; memos; , trade between countries: manufactured goods, raw materials, political interactions between countries (NY times data): joint ventures/mergers among companies; interlocking directorates Survey Research

Network Data Collection Techniques 1Survey 2EgocentricSocial roles Name generators and questions on the interaction between those named 3SequencedSnowball Name generator and interview those named 4CensusRoster 5Two-mode or joint Nominations of events attended or organziational membership

Data Collection Name generator. – Please name up to five organizations that you admire most for providing high quality health services to patients in Phoenix area. Relation-based: – “Which organizations do you have contracts with? " Time. – Cross-sectional or longitudinal network study.

Data Collection: Name-Generator. We are interested in learning about people you contact when you need assistance with questions about diabetes self-care. Think of the people who acted as a critical source of knowledge for you regarding diabetes care during the past year. Please name up to six persons (use the space below to add more names). His/her area of expertise Name and location of his /her work organization His/her influence in the field of diabetes care 1=low, 2=high, 3=very high (Please circle) Frequency of your communication with him/her. 1=low, 2=high, 3=very high Level of trust in your relationship with him/her. 1=low, 2=high, 3=very high Subject of your discussion. 1. ______ ______ ______ ______ ______ ______ 1 2 3

Network Data Collection Listed below are organizations in (name of community) that we believe are involved in some way in the provision of health and support services for chronic diseases. We would like to know the extent to which your organization is involved with, or linked to, the others on the list for providing a full range of services to patients/clients who have or might have a chronic disease like diabetes, cancer, heart disease, etc.

R R R R R R R R R R R R R R R A A A A A A A A A A A A A A R R R R R R R R R R R R R R R A A A A A A A A A A A A A A Matrix Visualization Show Relationships Question: Who do you work with? A “1” indicates the presence of a relationship. A “0” represents the absence of a relationship.

Network Data Characteristics The network question What types of relationships to ask? Directionality Symmetric vs. asymmetric Confirmed vs. unconfirmed Weight Binary or valued

Data Analysis Network visualization Description of a relational network/matrix in structural terms (dyad, clique, network component, and whole-network level). Network variable as outcome or independent variable in multivariate analysis.

Network Graph of Referrals 0-4 ties= blue node, 5-9 ties= red node (degree centrality) Thick Line= frequent interaction Circle= Non-profit, Square= for profit, Up triangle= public Orange dotted line= Structural Hole Green Line= Bridging ties (connecting otherwise disconnected network parts)

Network Analysis Random Permutation Methods – QAP Correlation and Regression – Node-level Analysis (ANOVA, t test and regression) t/C18_Statistics.html#twor

Network Analysis Exponential Random Graph Models (ERGM) – Do network structural properties occur in a network more than expected by chance? – Is there an association between network links and behavior? Chapter 9 in Valente, T.W Social Networks and Health. Oxford University Press.

Resources for Network Analysis Articles – Borgatti, S.P Network analysis in the social sciences. Science, 323, Feb 13, pp Textbooks – Kilduff & Tsai, 2003, “Social Networks and Organizations” – Valente, T.W., 2010 “Social Networks and Health” – Hanneman & Riddle, 2005, “ Introduction to Social Network Methods”. (faculty.ucr.edu/~hanneman/nettext/Introduction_to_Social_Network_Meth ods.pdf)