%0 Journal Article
	%A A. Melka and  N. Slater and  A. Mualem and  Y. Louzoun
	%D 2019
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 145, 2019
	%T Natural Emergence of a Core Structure in Networks via Clique Percolation
	%U https://publications.waset.org/pdf/10009965
	%V 145
	%X Networks are often presented as containing a “core”
and a “periphery.” The existence of a core suggests that some
vertices are central and form the skeleton of the network, to which
all other vertices are connected. An alternative view of graphs is
through communities. Multiple measures have been proposed for
dense communities in graphs, the most classical being k-cliques,
k-cores, and k-plexes, all presenting groups of tightly connected
vertices. We here show that the edge number thresholds for such
communities to emerge and for their percolation into a single dense
connectivity component are very close, in all networks studied. These
percolating cliques produce a natural core and periphery structure.
This result is generic and is tested in configuration models and in
real-world networks. This is also true for k-cores and k-plexes. Thus,
the emergence of this connectedness among communities leading to
a core is not dependent on some specific mechanism but a direct
result of the natural percolation of dense communities.
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