A Survey of Statistical Methods for Graph Analysis

Only recently have statistical models and methods been developed that begin to meet the need for proper handling of sampling variation, measurement errors, and other kinds of uncertainty in network data.

Abstract

Sociometric problems involving empirical sociograms and more general networks have been one of the major sources of an increasing interest in statistical graph models. The well-known book by Harary, Norman, and Cartwright (1965) has contributed much to the mathematical modeling of social networks, and we now find numerous methodological articles appearing in the literature-for instance, in the Journal of Mathematical Sociology, Social Networks, and other professional journals. Nonetheless, while statistical testing and estimation problems are discussed in some reports, statistical issues are all too often ignored or treated in a very elementary way. Only recently have statistical models and methods been developed that begin to meet the need for proper handling of sampling variation, measurement errors, and other kinds of uncertainty in network data.