Distributional Aspects of Some Statistics in Weighted Social Networks

Abstract

Social network researchers often have to consider the weight (in the sense of strength or intensity of interaction) of each tie of a network, but the data on weights of the ties in a network cannot be represented by a digraph. Instead, a multidigraph has to be used in such cases. Then, imposing some conditions and assumptions, we have introduced four multinomial-type probabilistic models for weighted social networks and studied the distributional aspects of some statistics (e.g., number of sources, numbers of sinks, and number of isolates).

Keywords:

• isolate
• loop
• reciprocity count
• sink
• source

ACKNOWLEDGMENTS

The authors are sincerely grateful to late Professor A. R. Rao and late Prof. Suraj Bandyopadhyay for suggesting the problem with solution outline and also to Professor Bikas K. Sinha for his valuable suggestions and comments on the article. The authors also express their sincere gratitude to the reviewers for their valuable comments and suggestions towards enrichment of the article.