Graph embedding in vector spaces by node attribute statistics
Pattern Recognition
Invariants of distance k-graphs for graph embedding
Pattern Recognition Letters
Feature selection on node statistics based embedding of graphs
Pattern Recognition Letters
Graph complexity from the jensen-shannon divergence
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Graph characterization using gaussian wave packet signature
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Analysis of the schrödinger operator in the context of graph characterization
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Entropy and heterogeneity measures for directed graphs
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Depth-based complexity traces of graphs
Pattern Recognition
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The novel contributions of this paper are twofold. First, we demonstrate how to characterize unweighted graphs in a permutation-invariant manner using the polynomial coefficients from the Ihara zeta function, i.e., the Ihara coefficients. Second, we generalize the definition of the Ihara coefficients to edge-weighted graphs. For an unweighted graph, the Ihara zeta function is the reciprocal of a quasi characteristic polynomial of the adjacency matrix of the associated oriented line graph. Since the Ihara zeta function has poles that give rise to infinities, the most convenient numerically stable representation is to work with the coefficients of the quasi characteristic polynomial. Moreover, the polynomial coefficients are invariant to vertex order permutations and also convey information concerning the cycle structure of the graph. To generalize the representation to edge-weighted graphs, we make use of the reduced Bartholdi zeta function. We prove that the computation of the Ihara coefficients for unweighted graphs is a special case of our proposed method for unit edge weights. We also present a spectral analysis of the Ihara coefficients and indicate their advantages over other graph spectral methods. We apply the proposed graph characterization method to capturing graph-class structure and clustering graphs. Experimental results reveal that the Ihara coefficients are more effective than methods based on Laplacian spectra.