Toward Quantifying Vertex Similarity in Networks

Q3 Mathematics
Charalampos E. Tsourakakis
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引用次数: 13

Abstract

Abstract Vertex similarity is a major concept in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices (graph matching). With respect to the former problem, we propose to optimize a geometric objective that allows us to express each vertex uniquely as a convex combination of a few extreme types of vertices. Our method has the important advantage of supporting efficiently several types of queries such as, which other vertices are most similar to this vertex? by using appropriate data structures and by mining interesting patterns in the network. With respect to the latter problem (graph matching) we propose the generalized condition number—a quantity widely used in numerical analysis— κ(LG, LH) of the Laplacian matrix representations of G, H as a measure of graph similarity, where G, H are the graphs of interest. We show that this objective has a solid theoretical basis, and, we propose a deterministic and a randomized graph alignment algorithm. We evaluate our algorithms on both synthetic and real data. We observe that our proposed methods achieve high-quality results and provide us with significant insights into the network structure.
网络中顶点相似度的量化
顶点相似度是网络科学中的一个重要概念,有着广泛的应用。在这项工作中,我们提供了在网络内和具有相同顶点数量的两个网络(图匹配)中寻找(非)相似顶点的新视角。对于前一个问题,我们建议优化一个几何目标,使我们能够将每个顶点唯一地表示为几个极端类型顶点的凸组合。我们的方法有一个重要的优势,它有效地支持多种类型的查询,例如,哪些其他顶点与这个顶点最相似?通过使用合适的数据结构和挖掘网络中有趣的模式。对于后一个问题(图匹配),我们提出了广义条件数-一个在数值分析中广泛使用的量- κ(LG, LH)的拉普拉斯矩阵表示G, H作为图相似度的度量,其中G, H是感兴趣的图。我们证明了这一目标具有坚实的理论基础,并提出了一种确定性和随机化的图对齐算法。我们在合成数据和真实数据上对我们的算法进行了评估。我们观察到我们提出的方法获得了高质量的结果,并为我们提供了对网络结构的重要见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Internet Mathematics
Internet Mathematics Mathematics-Applied Mathematics
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