Article

On Modularity Clustering

Univ. of Konstanz, Konstanz
IEEE Transactions on Knowledge and Data Engineering (Impact Factor: 2.07). 03/2008; 20(2):172 - 188. DOI: 10.1109/TKDE.2007.190689
Source: IEEE Xplore

ABSTRACT

Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomerative approach.

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    • "For the automatic network clustering, the most popular criterion function is the modularity (denoted as Q) presented by Newman and Girvan [26] [27]. A high value of Q represents a good partition [12] [26] [27]. By simply optimizing Q over all possible partitions, the best solution can be found. "
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    • "However, it needs the absolute best and worst fitness values in the search space. We adopted modularity [15] as fitness value, and it has been proved that its value ranges between -0.5 and 1 [17]. Of course these limit values depend on the network structure. "
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    • "However, it needs the absolute best and worst fitness values in the search space. We adopted modularity [15] as fitness value, and it has been proved that its value ranges between -0.5 and 1 [17]. Of course these limit values depend on the network structure. "
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