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oai:drum.lib.umd.edu:1903/183572017-06-13T10:33:54Zcom_1903_2234com_1903_1654com_1903_2col_1903_2765col_1903_3

Makowski, Armand Qu, Sikai Digital Repository at the University of Maryland University of Maryland (College Park, Md.) Electrical Engineering 2016-06-22T06:10:19Z 2016-06-22T06:10:19Z 2016 https://doi.org/10.13016/M2JF50 http://hdl.handle.net/1903/18357 Graphs are powerful tools to describe social, technological and biological networks, with nodes representing agents (people, websites, gene, etc.) and edges (or links) representing relations (or interactions) between agents. Examples of real-world networks include social networks, the World Wide Web, collaboration networks, protein networks, etc. Researchers often model these networks as random graphs. In this dissertation, we study a recently introduced social network model, named the Multiplicative Attribute Graph model (MAG), which takes into account the randomness of nodal attributes in the process of link formation (i.e., the probability of a link existing between two nodes depends on their attributes). Kim and Lesckovec, who defined the model, have claimed that this model exhibit some of the properties a real world social network is expected to have. Focusing on a homogeneous version of this model, we investigate the existence of zero-one laws for graph properties, e.g., the absence of isolated nodes, graph connectivity and the emergence of triangles. We obtain conditions on the parameters of the model, so that these properties occur with high or vanishingly probability as the number of nodes becomes unboundedly large. In that regime, we also investigate the property of triadic closure and the nodal degree distribution. en A comprehensive study of multiplicative attribute graph model Dissertation Electrical engineering Statistics Mathematics Log-normal degree distribution Modeling Random Graphs Social Network Zero-one laws open.access