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The network alignment (or graph matching) problem refers to recovering thenode-to-node correspondence between two correlated networks. In this paper, wepropose a network alignment algorithm which works without using a seed set ofpre-matched node pairs or any other auxiliary information (e.g., node or edgelabels) as an input. The algorithm assigns structurally innovative features tonodes based on the tail of empirical degree distribution of their neighbornodes. Then, it matches the nodes according to these features. We evaluate theperformance of proposed algorithm on both synthetic and real networks. Forsynthetic networks, we generate Erdos-Renyi graphs in the regions of$\Theta(\log(n)/n)$ and $\Theta(\log^{2}(n)/n)$, where a previous worktheoretically showed that recovering is feasible in sparse Erdos-Renyi graphsif and only if the probability of having an edge between a pair of nodes in oneof the graphs and also between the corresponding nodes in the other graph is inthe order of $\Omega(\log(n)/n)$, where $n$ is the number of nodes. Experimentson both real and synthetic networks show that it outperforms previous works interms of probability of correct matching.

Seedless Graph Matching via Tail of Degree Distribution for Correlated Erdos-Renyi Graphs