Chapter 2
Portions of this chapter originally appeared in Moldoveanu and Baum: “‘I Think You Think I Think You’re Lying’: Interactive Epistemology of Trust in Social Networks.” Management Science 57(2), 2011, pp. 393–412. Copyright 2011, Institute for Operations Research and the Management Sciences, 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA. Reprinted with permission.
Chapter 3
1. Degree centrality for faculty member i refers to the number of edges attached to the node—that is, the number of direct connections that i has. Betweenness centrality for faculty member i is Σjkσjk(i)/σjk, where σjk is the number of shortest paths between faculty members j and k, and σjk(i) is the number of shortest paths from j to k that pass through i. Eigenvector centrality, if faculty member i is defined proportional to the sum of the eigenvector centrality of i’s neighbors, is ei = Σj=nn(i)ej/λ, where nn(i) denotes the set of neighbors of faculty member i, which can be rewritten in matrix form A · e = λe, where A is the adjacency matrix of the faculty network, and e represents the vector of faculty centrality scores. Thus, e is the eigenvector of A relative to the eigenvalue λ.
2. We identified the cliques in each network using the N-clique procedure implemented in Ucinet 6.0 (Borgatti, Everett, and Freeman 2002). An N-clique is one in which the geodesic distance between all nodes is no greater than N for paths in a network subgraph. We set N = 1, thus defining clique members as directly tied to each other, and we set the minimum clique size to three faculty members.
3. Google centrality (Page et al. 1998) is a computationally simplified form of eigenvector centrality, computable for very large networks such as the World Wide Web in short enough periods of time to be useful to typical users.
Chapter 4
Portions of this chapter originally appeared in Moldoveanu and Baum: “‘I Think You Think I Think You’re Lying’”: Interactive Epistemology of Trust in Social Networks.” Management Science 57(2), 2011, pp. 393–412. Copyright 2011, Institute for Operations Research and the Management Sciences, 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA. Reprinted with permission.
1. We are grateful to Tim Rowley and Diederik van Liere for granting us access to the network data collected in the first phase, as well as for their assistance in the second phase with the collection of additional data used in the analysis of trust.
2. Betweenness for respondent i is Σjkσjk(i)/σjk, where σjk is the number of shortest paths from j to k, and σjk(i) is the number of shortest paths from j to k that pass through respondent i (Freeman 1977).
3. Constraint for respondent i is Σj(pij + Σq piq pjq)2, q ≠ i, j, pij is the strength of respondent i’s relationship with alter j, and piq and pjq are the strengths of alter q’s relationships with i and j, respectively (Burt 1992). When piq pjq is large, a strong third-party tie connects respondent i to alter j indirectly. Summing over q provides an assessment of the overall strength of third-party ties surrounding respondent i. Constraint varies from a minimum of pij, when alter j is disconnected from all of respondent i’s other alters, to a maximum of 1, when j is i’s only alter.
4. These factors were selected by the firm’s senior management.
5. Ideally, this final item would have been separated into two: one focused on competence and the other on integrity. They were combined at the request of the firm’s top management to shorten the survey.
6. Because we wanted to focus on significant ties, we did not include highly asymmetric reciprocal ties (i.e., where one respondent rated the tie of low significance; the other, of high significance).
7. Given the correlations among the variables, we report a set of hierarchically nested models to check whether multicollinearity was imposing a conservative bias on our estimates by inflating coefficient standard errors. The absence of such inflation is reinforced by variance inflation factor (VIF) statistics for each model, which reach a maximum of 1.34—well below the threshold of 10 (Belsley, Kuh, and Welsch 1980).
8. Again, neither model estimates nor VIF statistics reported for each model indicate multicollinearity concerns.