The analysis of complex networks is usually based on key properties such as small-worldness and vertex degree distribution. The presence of symmetric motifs on the other hand has been related to redundancy and thus robustness of the networks. In this paper we propose a method for detecting approximate axial symmetries in networks. For each pair of nodes, we define a continuous-time quantum walk which is evolved through time. By measuring the probability that the quantum walker to visits each node of the network in this time frame, we are able to determine whether the two vertices are symmetrical with respect to any axis of the graph. Moreover, we show that we are able to successfully detect approximate axial symmetries too. We show the efficacy of our approach by analysing both synthetic and real-world data.


Complex Network Symmetry Quantum Walk 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Luca Rossi
    • 1
  • Andrea Torsello
    • 1
  • Edwin R. Hancock
    • 2
  1. 1.Department of Environmental Science, Informatics and StatisticsCa’ Foscari University of VeniceItaly
  2. 2.Department of Computer ScienceUniversity of YorkUK

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