Local Graph Clustering and Applications to Graph Partitioning

Today there exist innumerable applications which require the analysis of some type of large graph. Social networks useful to social scientists, protein interaction and neural networks arising in biological problems, as well as geometric meshes used in many diverse scientific applications, have grown, thanks to the availability and abundance of data, to tremendous proportions. Besides the sheer size of some of these datasets – the world wide web, for example, is estimated to contain at least 4.75 billion pages [11] – the analysis of even moderately large networks, on the order of tens of thousands of vertices, poses a significant challenge when researches need information beyond basic metrics such as the degree distribution. The NP-complete problem of finding an optimal clustering of vertices within one of these networks, for example, has been under investigation for over a decade by various scientific communities, including data mining, computational biology, and combinatorics.