Network characterization and simulation via mixed properties of the Barabási–Albert and Erdös–Rényi degree distribution

Social network analysis (SNA) is a tool for the operations researcher to understand, monitor, and exploit social and military structures which are key in the intelligence community. However, in order to study and influence a network of interest, the network must first be characterized; preferably to a known network model that captures a mixture of graphical properties exhibited by the social network of interest. In this work, we present a novel statistical method for both characterizing networks via a Binomial-Pareto maximum-likelihood approach and simulating the characterized network using a graph of mixed Barabási–Albert (BA, scale-free) and Erdös–Rényi (ER, randomness) properties. Characterization is performed through a combination of hypothesis tests and method of moments parameter estimation on Pareto and Doubly Truncated Binomial distributions. Application on real-world networks suggests that such networks may be characterized with a mixture of scale-free and random properties as modeled through BA and ER graphs. We demonstrate that our simulation methods are able to capture the degree distribution and density of the networks examined. These results demonstrate that this work establishes a statistical framework upon which network characterization and simulation may be accomplished, thus enabling the adaptation of such methods when generating, manipulating, and observing networks of interest.