Determining the connectedness of an undirected graph

doi:10.7523/j.issn.2095-6134.2018.05.002

›› 2018, Vol. 35 ›› Issue (5): 582-588.DOI: 10.7523/j.issn.2095-6134.2018.05.002

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Determining the connectedness of an undirected graph

TAN Tunzi, GAO Suixiang, YANG Wenguo

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;Key Laboratory of Big Data Mining and Knowledge Management of Chinese Academy of Sciences, Beijing 100190, China

Received:2017-02-18 Revised:2017-11-15 Online:2018-09-15
Supported by:
Supported by the National 973 Plan project(2011CB706900), the National 863 Plan project (2011AA01A102), the NSFC (11331012,11571015) and the "Strategic Priority Research Program" of Chinese Academy of Sciences (XDA06010302)

Abstract

Abstract: Determining the connectedness of an undirected graph is a frequent issue in practical graph mining and regarded as a key subproblem of the graph partitioning problem. Apart from graph partitioning, graph connectedness also plays an imperative role in tracking the spread of disease, VLSI design, social network analysis, and theoretical studies in graph theory such as "Cayley graph". This work reviews several important methods for determining the connectedness of an undirected graph, such as breadth-first search, depth-first search, and the eigenvalues of a graph Laplacian matrix. In addition, we propose several new methods, such as power sum and logical sum of adjacency matrix. We compare all the relevant methods empirically on random graphs with up to 10 000 vertices, and show that the breadth-first search and logical sum methods deliver good performances on large graphs with more than 100 vertices and the logical sum method is the fastest.

Key words: connectedness, breadth-first search, depth-first search, power sum, Laplacian matrix, logical sum

CLC Number:

O157.5

TAN Tunzi, GAO Suixiang, YANG Wenguo. Determining the connectedness of an undirected graph[J]. , 2018, 35(5): 582-588.

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