Aproximativní symmetrie komplexních sítí

Straka, Matej

The aim of this thesis is to investigate the problem of an approximate symmetry of complex networks. First, we analyze how to measure such symmetry. Then we explore two algorithms by which we can measure levels of symmetry of networks and also find permutations representing those symmetries. First method uses a simulated annealing algorithm which is very slow if implemented naively. We exploit properties of an objective function to make this approach much faster, making it usable for large networks. In second approach we modify an existing method for inexact graph matching, making it applicable for measuring symmetry. We then provide a comparison of these two approaches. We then apply these algorithms to explore levels of symmetry produced by artificial networks, which are used to generate networks with properties possessed by real sys- tems. We explore how does our measure of an approximate symmetry correlate with other network measures, such as clustering coefficient or modularity. Finally, we measure symmetry of real brain networks and look where their symmetry comes from. 1

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