Computing Communities in Large Networks Using Random Walks. Pons, P. & Latapy, M. In Yolum, p., Güngör, T., Gürgen, F., & Özturan, C., editors, Computer and Information Sciences - ISCIS 2005, of Lecture Notes in Computer Science, pages 284–293, Berlin, Heidelberg, 2005. Springer.
doi  abstract   bibtex   
Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, it works at various scales, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm which runs in time O(mn2) and space O(n2) in the worst case, and in time O(n2log n) and space O(n2) in most real-world cases (n and m are respectively the number of vertices and edges in the input graph).
@inproceedings{pons_computing_2005,
	address = {Berlin, Heidelberg},
	series = {Lecture {Notes} in {Computer} {Science}},
	title = {Computing {Communities} in {Large} {Networks} {Using} {Random} {Walks}},
	isbn = {978-3-540-32085-2},
	doi = {10.1007/11569596_31},
	abstract = {Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, it works at various scales, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm which runs in time O(mn2) and space O(n2) in the worst case, and in time O(n2log n) and space O(n2) in most real-world cases (n and m are respectively the number of vertices and edges in the input graph).},
	language = {en},
	booktitle = {Computer and {Information} {Sciences} - {ISCIS} 2005},
	publisher = {Springer},
	author = {Pons, Pascal and Latapy, Matthieu},
	editor = {Yolum, pInar and Güngör, Tunga and Gürgen, Fikret and Özturan, Can},
	year = {2005},
	keywords = {Community Detection, Community Structure, Large Network, Physical Review, Random Walk},
	pages = {284--293},
}

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