Classical Statistical Inference for the Reliability of a Co-Authorship Network with Emphasis on Edges
Beatriz Barbero Brigantini, Sandra Cristina de Oliveira, Sergio Silva Braga Junior

Abstract
Highly reliable research groups, i.e., with a strong collaborative framework of researchers, may contribute widely and intensely for the emergence and/or implementation of ideas, since they are responsible for most current research and also for the formation of numerous researchers. A research group may be considered a social network, which may be modeled by a graph. Researchers that make up this network may be interpreted as its nodes or actors, and the connections or links between these agents (represented by publications in common, i.e., co-authored papers) may be considered as its edges. In the literature, there are some ways to calculate the reliability of a network modeled by a graph G with k nodes and m edges. Current analysis measures the reliability of networks by taking into consideration unreliable edges and perfectly reliable nodes. Specifically, a statistical analysis based on classical inference to the network reliability has been proposed, obtaining the maximum likelihood estimators and confidence intervals for individual components (edges) and the network (probability of the research group to remain in activity at a given time t); the proposed methodology was applied to a research group of UNESP registered at CNPq; and measures of centrality of nodes were obtained to identify situations in which the insertion of an edge (connection between two researchers of the group) could significantly increase the reliability of a co-authoring network. Results show the feasibility of classical statistical inference coupled with the use of measures of centrality in the context of social network analysis.

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