Journal of Statistical Mechanics: Theory and Experiment
Volume 2006
September 2006
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I Ispolatov et al J. Stat. Mech. (2006) P09014 doi:10.1088/1742-5468/2006/09/P09014
Finding mesoscopic communities in sparse networks
I Ispolatov1, I Mazo and A Yuryev
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| Figure 1. Cluster size histogram for the fly network. The cluster abundance for α = 1.5 and γ = 10–2 (red dotted line) strongly peaks around the desired community size, n ≈ 15, while the histogram for the same α and smaller γ = 10–3 (dashed black line) consists of a smaller and broader peak at much larger clusters, n ≈ 50. While clustering with a smaller antiferromagnetic exponent, α = 0.5 and γ = 0.2 (green solid line) also produces a cluster size distribution with a maximum at a desired cluster size, n ≈ 15, the number of such clusters is noticeably less than in the α = 1.5 and γ = 10–2 case, and very large (up to n = 200) biologically irrelevant clusters are produced. Only clusters consisting of n > 8 vertices and L > 2n links are counted; the results are averaged over 50 equilibration runs. |
| Figure 2. Top to bottom: An mRNA splicing complex in a yeast network. Two examples of densely linked clusters in the fly network. On top is the mini-chromosome maintenance complex. Clustered vertices, marked with blue haloes, are shown together with their nearest neighbours. Note only a single link between the neighbours. On the bottom is a cluster, formed around five recently duplicated and thus highly similar (paralogous) heat-shock proteins. The large link density is produced by the duplicated (paralogous) links from heat-shock proteins to their partners. The yeast network is a union of data from [7, 8] and consists of N = 3689 vertices and L = 5551 links. The fly network is taken from [9] and spans N = 6954 vertices with L = 20 435 links. |
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Finding mesoscopic communities in sparse networks
I Ispolatov et al J. Stat. Mech. (2006) P09014
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