There is a virtual agreement that the world has become more complex and that it is very difficult to construct knowledge individually. The stimulus to the formation of research groups - by universities and funding agencies - attests to this reality. Therefore, highly reliable research groups, ie, a structure with strong collaboration of researchers, can contribute widely and intensively in the development and/or implementation of ideas, since they are responsible for most of the current investigations and also for the formation of numerous researchers. A research group can be considered a social network, which can be modeled by a graph. In literature, there are some ways to calculate the reliability of a system modeled by a graph G composed by n vertices and k edges. The purpose of this work is to obtain the reliability of systems considering the vertices (researchers who make up a research group) perfectly reliable and only the edges (connections between these agents) unreliable or prone to failure, and to present a statistical analysis based on classical inference to calculate the reliability of systems, and in this context, to present some measures of centrality of vertices that will assist in identifying situations where the insertion of one or more edges can increase the reliability of systems. The methodology is illustrated by a fictitious system and two special cases of social network of researchers, ie, UNESP research groups registered in the CNPq.
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