Date of Award:


Document Type:


Degree Name:

Master of Science (MS)


Mathematics and Statistics


David E. Brown


Graph theory is the foundation on which social network analysis (SNA) is built. With the flood of "big data," graph theoretical concepts and their linear algebraic counterparts are essential tools for analysis in the burgeoning field of network data analysis, in which SNA is a subset. Here we begin with an overview of SNA. We then discuss the common descriptive measures taken on network data as well as proposing new measures specific to homeless networks. We also define a new data structure which we call the location sequence matrix. This data structure makes certain computational network analyses particularly easy. Finally we apply Pulse Processes in a new way to the homeless network in Utah. We believe the new data structure and pulse processes, when used for analysis of the Utah homeless services. In particular, pulse processes, first introduced by Brown, Roberts, and Spencer, to analyze energy demand, form a dynamic population model that can provide a measure of the stability in a network and the patterns of action of individuals experiencing homelessness.



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