Unformatted text preview: etworks. Our studies of
n and protein interaction graphs
ies has non-trivial correlations and
contain parts in which the nodes
ted to each other than to the rest of
nodes are usually called clusters,
or modules8,10,11–13; they have no
ition. In spite of this ambiguity,
in networks is a signature of the
systems5,14. The existing methods
e networks are useful if the commube interpreted in terms of separated
b and refs 10, 15, 16–18). However,
terized by well-deﬁned statistics of
nities. This can be illustrated by the
ch of us belongs to, including those overlapping
Nature, 435 k-clique aggregation (Palla et al.) Figure 1 | Illustration of the concept of overlapping communities. a, The
black• Build up k-cliques. either of the authors overlapping ith
dot in the middle represents k-cliques with of this paper, w nodes
several of his communities around. Zooming in on the scientiﬁc community
demonstrates the nested and overlapping structure of the communities, and
depicting the cascades of communities starting from some members
exempliﬁes the interwoven structure of the network of communities.
• What size k to choose? (Typically try 2, 3, 4, 5)
b, Divisive and agglomerative methods grossly fail to identify the
communities when overlaps are signiﬁcant. c, An example of overlapping
• communities at k assigned to communities
k-cliqueNot all nodes ¼ 4. The yellow community overlaps the blue one
in a single node, whereas it shares two nodes and a link with the green one.
These overlapping regions are emphasized in red. Notice that any k-clique
(complete subgraph of size k) can be reached only from the k-cliques of the are in overlapping Aggregating/collapsing:
treat k-cliques as nodes and recurse
H.-W. Shen, X. Cheng, K. Cai, and M.-B. Hu, Physica A 388, 1706 (2009).
• Find maximal k-clique, collapse into one node
• Repeat until all nodes now assigned to a clique Noise in community detection
Haoran Wen, E. A. Leicht, and R. M. D’Souza, “Improving community detection in networks
HAORAN WEN, E. A. LEICHT, AND RAISSA M. D’SOUZA
by targeted node removal” Physical Review E 83, 016114, 2011.
(a) (b) networks but has no
to one-quarter o...
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