Algebraic Distance on Graphs
نویسندگان
چکیده
Abstract. Measuring the connection strength between a pair of vertices in a graph is one of the most vital concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the local connectivity. In this paper, we consider an iterative process that smoothes an associated value for nearby vertices, and present a measure of the connection strength (called the algebraic distance, see [28]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process confirms the underlying intuition that vertices are mutually reinforced and that the local neighborhoods play an important role in influencing the vertex connectivity. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.
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عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 33 شماره
صفحات -
تاریخ انتشار 2011