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Journal Articles Journal of Complex Networks Year : 2017

Evaluating balance on social networks from their simple cycles

P.-L Giscard
Paul Rochet
  • Function : Author
Richard Wilson
  • Function : Author

Abstract

Simple cycles, also known as self-avoiding polygons, are cycles on graphs which are not allowed to visit any vertex more than once. We present an exact formula for enumerating the simple cycles of any length on any directed graph involving a sum over its induced subgraphs. This result stems from an Hopf algebra, which we construct explicitly, and which provides further means of counting simple cycles. Finally, we obtain a more general theorem asserting that any Lie idempotent can be used to enumerate simple cycles.

Dates and versions

hal-03597455 , version 1 (04-03-2022)

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P.-L Giscard, Paul Rochet, Richard Wilson. Evaluating balance on social networks from their simple cycles. Journal of Complex Networks, 2017, 341 (5), pp.1439-1448. ⟨10.1093/comnet/cnx005⟩. ⟨hal-03597455⟩
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