Network Data: an overview Introduction to Graph Theory and Sociometric Notation Dante J. Salto & Taya L. Owens 6 February 2013 Rockefeller College RPAD 637
Works Summarized Wasserman, S. & Faust, K. (2009). Social network analysis: Methods and applications, structural analysis in the social sciences. New York, NY: Cambridge University Press. (Ch 3&4) Marsden, P.V. (1987). Core discussion networks of Americans. American Sociological Review, 52(1): 122-131. Rethemeyer, R.K. (2005). Conceptualizing and measuring collaborative networks. Public Administration Review, 65(1): 117-121.
Notation Schemes Graph Theoretic Notation (GTN) simplest, visual, descriptive Sociometric Notation (SmN) most common in SNA literature Algebraic Notation (AN) least common, most complex, inferential
Sociometric Notation Sociometric networks consist of people and their measured affective relations
SmN Relational data is often presented in two-way matrices termed sociomatrices Alice Bob Carol David Alice - 0 1 1 Bob 0-1 1 Carol 1 0-0 David 1 1 0 - receiving sending
Applied sociometry: a brief example Who in this room would you choose 2 requirements: 1. Choose only one person 2. You must choose someone. Source: http://www.hoopandtree.org/sociometry.htm
Applied sociometry: a brief example Star: most frequently chosen Mutuals: two people choose each other Chains: A B C D Gaps & cleavages: Clusters have chosen each other but are isolated from other clusters Describe, interpret, modify? Source: http://www.hoopandtree.org/sociometry.htm
Graph theoretic An overview Elementary way to represent actors and relations Centrality and prestige methods Cohesive subgroup ideas Dyadic and triadic methods Based on graph theory
Single Relation Set of actors/nodes (N) Actors/nodes of a network (n) Set of connections/arcs (L) Connections/arc of a network (l) Source: http://labspace.open.ac.uk/mod/resource/view.php?id=378588
Connections Graphs consists of nodes (n) and connections (l) Source: http://labspace.open.ac.uk/mod/resource/view.php?id=378588
Types of connections (notations) Directional <, > Non-directional (, )
Directional Connections <, > Source: http://labspace.open.ac.uk/mod/resource/view.php?id=378588
Directional Graph <, >
Non-directional Connections (, ) Source: http://labspace.open.ac.uk/mod/resource/view.php?id=378588
Nodal Degree
Walks, trails and paths Source: http://labspace.open.ac.uk/mod/resource/view.php?id=378588
Examples International Collaboration in Science: The Global Map and the Network http://www.leydesdorff.net/intcoll/intcoll.htm http://www.leydesdorff.net/map06/index.htm
Core Discussion Networks of Americans Marsden (1987) American Sociological Review Describes the features of core social networks: important relationships Network measures Size Density Heterogeneity General Social Survey (GSS, 1985) N=1,531
Core Discussion Networks of Americans Typical: Small, centered on kin, dense and homogeneous. Well-educated, young & middle-aged people living in urban areas have more diverse networks. So what?
Conceptualizing and measuring collaborative networks Rethemeyer (2005) Public Administration Review Book reviews: Managing Complex Networks Getting Results through Collaboration Collaborative Public Management
Conceptualizing and measuring collaborative networks Normative analysis: Networks as a policy instrument Make it happen Collaborative advocates active use, positioning horizontal against vertical. Don t mess with it Managing assumes networks are integral to policy. Getting Results describes case-studies, emphasis on context and culture.
Conceptualizing and measuring collaborative networks The role of public managers Make it happen Don t mess with it Managing assumes managers are facilitators. Collaborative suggests managers can orchestrate networks. Getting Results suggest that managerial roles depend on national histories and culture.
Conceptualizing and measuring collaborative networks Lack of social analytic tools Indirect connections: The structure of indirect connections can determine, for instance, whether government or private sector actors can control information and resource flows, which may affect the payoff to participants in collaborative endeavors. To some extent, what the authors have tried to do in these three volumes is the equivalent of trying to study a monopoly without knowing whether the monopolist sells into a market of one or one thousand. The structure of the market matters in a monopoly; the structure of indirect connections may matter in collaboration. (p.120)