Clustering assortativity, communities and functional modules in real-world networks

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.

Network analysis of the Íslendinga sögur – the Sagas of Icelanders

“…2 The networks each exhibit clustering assortativity (signalled by r C > 0). This is also a common feature of realworld networks, both social and non-social [27]. In Ref.…”

“…It has been suggested that networks other than real social networks tend to be disassortatively mixed by degree [6]. Real-world networks are also found to have high clustering assortativity r C and it has been suggested that this also indicates the presence of communities [27].…”

“…In Ref. [27], it is also suggested that a high value of r C is a potential indicator for the presence of communities. Egils saga and Laxdaela saga indeed have high r C -values and contain strong community structure.…”

Toward Structural Controllability and Predictability in Directed Networks

“…This data can be accessed via [50]. 8) Guava [51]: Guava library dependencies is a network of software dependencies in Guava r07 core libraries. Nodes represent libraries, and a directed link indicates a dependency of one library on another.…”