Structurally Induced Random Graph Model of Social Networks

As promised, here is the draft paper of my research on a new random graph model entitled, “Structurally Induced Random Graph Model of Social Networks” As always, I welcome your questions, comments and critiques.

The research and development of random graph models of social networks has provided great insight into the dynamics of complex network systems. The primary shortcoming of these models; however, is their treatment of the atomistic component of a network—the vertex. These models assume vertices exist in a vacuum, bringing no exogenous structure to the network system and only forming endogenous structure once inside a network. This assumption is entirely contrary to the fundamental dynamics of social interaction observed in nearly all settings. The following research attempts to bridge the gap between current random graph models of social networks and the process by which individuals form new social structure in the real world. This paper presents a new random graph modeling framework deemed the “structurally induced random graph model”, or SIRG, which is derived from two key assumptions. First, actors do not enter networks as isolates; and second, new structure in a network will resemble previously observed structure in that network. This simple framework provides a powerful platform upon which any number of models could be specified. The paper proceeds as follows: A brief review of the literature on random graph models is provided. The basic framework of the SIRG model is then presented, which is followed by a description of a single algorithmic implementation. Next, results from this implementation are presented, including several example networks generated by the model. Concluding remarks focus on the benefits of this model over the current family of models and future research.

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