One way of characterizing the topological and structural properties of vertices and edges in a graph is by using structural similarity measures. Measures like Cosine, Jaccard and Dice compute the similarities restricted to the immediate neighborhood of the vertices, bypassing important structural properties beyond the locality. Others measures, such as the generalized edge clustering coefficient, go beyond the locality but with high computational complexity, making them impractical in large-scale scenarios. In this paper we propose a novel similarity measure that determines the structural similarity by dynamically diffusing and capturing information beyond the locality. This new similarity is modeled as an iterated function that can be solved by fixed point iteration in super-linear time and memory complexity, so it is able to analyze large-scale graphs. In order to show the advantages of the proposed similarity in the community detection task, we replace the local structural similarity used in the SCAN algorithm with the proposed similarity measure, improving the quality of the detected community structure and also reducing the sensitivity to the parameter @math of the SCAN algorithm.
Another popular dynamic similarity based on the random walk intuition is SimRank @cite_11 . SimRank defines structural-context similarity of vertices (directly connected by edges or not) recursively as follows: . The SimRank is modeled as a recursive function solved by fixed point iteration. By definition, SimRank only works for directed graphs, and also requires a decay factor @math in order to control the flow of information in the dynamic system and to achieve convergence.
@cite_11
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The problem of measuring "similarity" of objects arises in many applications, and many domain-specific measures have been developed, e.g., matching text across documents or computing overlap among item-sets. We propose a complementary approach, applicable in any domain with object-to-object relationships, that measures similarity of the structural context in which objects occur, based on their relationships with other objects. Effectively, we compute a measure that says "two objects are similar if they are related to similar objects:" This general similarity measure, called SimRank, is based on a simple and intuitive graph-theoretic model. For a given domain, SimRank can be combined with other domain-specific similarity measures. We suggest techniques for efficient computation of SimRank scores, and provide experimental results on two application domains showing the computational feasibility and effectiveness of our approach.