Networks analysis, complexity, and brain function
Complexity - Special issue: Selection, tinkering, and emergence in complex networks
Note: Symmetry in complex networks
Discrete Applied Mathematics
Graph embedding using quantum commute times
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Coined quantum walks lift the cospectrality of graphs and trees
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
The Structure of Complex Networks: Theory and Applications
The Structure of Complex Networks: Theory and Applications
Analysis of the schrödinger operator in the context of graph characterization
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Attributed graph similarity from the quantum jensen-shannon divergence
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
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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.