Topological Properties of Exponential Random Graphs

Student: Kostiushina Anastasiia

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Year of Graduation: 2018

The paper studies the models of exponential random graphs in which the probability of occurrence of a specific implementation P(G) is proportional to e^(-H (G)), where H(G) is called the Hamiltionian. The function H(G) depends on the topological characteristics of the graph. We consider models where the number of edges, the number of triplets and the number of triangles of the graph are taken for these characteristics. In the paper the two phase states of the considered models were analytically demonstrated, depending on the parameters. Also, the existence of the phase transition has been confirmed numerically by the Monte Carlo method.

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