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The topological information of a network can be retrieved equivalently fromits complement consisting of the same nodes but complementary edges. Hence thepartition of a network into certain substructures based on given criteriashould be the same as that of its complement based on the equivalent criteriaif the topological information is considered exclusively. This symmetry ofpartitioning between a network and its complement is due to the equivalence oftheir topological information and hence should be respected regardless of thedetailed characteristics of the substructures considered. In this work wesuggest this symmetry consideration as a general guideline and propose asymmetric community detection scheme to show its implications. Our method hasno resolution limit and can be used to detect hierarchical community structuresat different levels. Our study also suggests that the community structure isunlikely a result of random fluctuations in large networks.

Symmetry consideration in identifying network structures