Misc,
Clustering assortativity, communities and functional modules in real-world networks
(2012)cite arxiv:1202.3188Comment: 21 pages, 15 figures, 7 tables.
Abstract
Complex networks of real-world systems are believed to be controlled by
common phenomena, producing structures far from regular or random. Clustering,
community structure and assortative mixing by degree are perhaps among most
prominent examples of the latter. Although generally accepted for social
networks, these properties only partially explain the structure of other
networks. We first show that degree-corrected clustering is in contrast to
standard definition highly assortative. Yet interesting on its own, we further
note that non-social networks contain connected regions with very low
clustering. Hence, the structure of real-world networks is beyond communities.
We here investigate the concept of functional modules---groups of regularly
equivalent nodes---and show that such structures could explain for the
properties observed in non-social networks. Real-world networks might be
composed of functional modules that are overlaid by communities. We support the
latter by proposing a simple network model that generates scale-free
small-world networks with tunable clustering and degree mixing. Model has a
natural interpretation in many real-world networks, while it also gives
insights into an adequate community extraction framework. We also present an
algorithm for detection of arbitrary structural modules without any prior
knowledge. Algorithm is shown to be superior to state-of-the-art, while
application to real-world networks reveals well supported composites of
different structural modules that are consistent with the underlying systems.
Clear functional modules are identified in all types of networks including
social. Our findings thus expose functional modules as another key ingredient
of complex real-world networks.
