Home Sociology Exponential Random Graph Models for Social Networks Theory, Methods, and Applications
In each type of friendship network, eight Markov parameters of directed networks were included as purely structural effects: “arc,” “reciprocity,” “in-2-star,” “out-2-star,” “2-path,” “transitive triad” (030T), “cyclic triad” (030C), and “transitive-cyclic triad” (120C) (see Figure 19.1). In a friendship network, the transitive triad parameter reflects the degree of transitive clustering (path closure), and the cyclic triad parameter is interpreted as a measure of the generalized exchange (cyclic closure) cycle (Lazega & Pattison, 1999). The transitive-cyclic parameter (120C) is not often used in ERGMs but here examines the extent to which path and cyclic closure is associated with reciprocity.
A total of seven actor-relation effects were included in the model. Parameters included homophily, sender and receiver effects for gender, and sender and receiver effects for IDMEMBER and IDgRoUP, respectively.
A longitudinal ERGM with eight structural effects and seven actor- relation effects was fitted separately for four types of networks. Overall, all models successfully converged and fitted the data well. Results of
(perhaps is likely to) vary over time, but under the assumption that these changes may be considered exogenous and that social selection is the predominant process, the researcher may choose to use only one measurement.
Changes in Face-to-Face and Text Message Networks
Table 19.1. Parameter estimates and standard errors in face-to-face friendship networks
the parameter estimation in the face-to-face and text message-mediated friendship networks are presented in Tables 19.1 and 19.2, respectively.
In all types of networks, the positive and significant effects of reciprocity indicated the strong tendency of mutual and direct exchange. Regardless of communication media and intimacy, positive and significant effects of transitive triads and negative and significant 2-path effects were consistently found, suggesting that indirect links between two people rarely occurred when controlling for other structural effects, especially given transitive path closure. These results indicated the strength of the purely structural processes in network evolution when controlling for the effect of gender homophily.
Except for text message-mediated self-disclosing networks, the positive effects of cyclic triads and the negative effects of transitive-cyclic triad were significant. These results suggested the emergence of cyclic closure through network evolution in face-to-face superficial/self-disclosing and text message-mediated superficial networks.
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