A novel characterization of amalgamated networks in natural systems.

Victor J Barranca,David Cai,Douglas Zhou

doi:10.1038/srep10611

Abstract

Densely-connected networks are prominent among natural systems, exhibiting structural characteristics often optimized for biological function. To reveal such features in highly-connected networks, we introduce a new network characterization determined by a decomposition of network-connectivity into low-rank and sparse components. Based on these components, we discover a new class of networks we define as amalgamated networks, which exhibit large functional groups and dense connectivity. Analyzing recent experimental findings on cerebral cortex, food-web, and gene regulatory networks, we establish the unique importance of amalgamated networks in fostering biologically advantageous properties, including rapid communication among nodes, structural stability under attacks, and separation of network activity into distinct functional modules. We further observe that our network characterization is scalable with network size and connectivity, thereby identifying robust features significant to diverse physical systems, which are typically undetectable by conventional characterizations of connectivity. We expect that studying the amalgamation properties of biological networks may offer new insights into understanding their structure-function relationships.

Highlights

With advances in technology and mathematical theory increasingly facilitating the study of complex networks, recent experimental evidence suggests that many networks are more densely-connected than previously proposed
Since these networks are resilient to node attacks, preserving overall network structure and activity fundamental for biological function, they have likely remained pervasive in many physical systems and may give significant insight into their characteristics
A network composed of m disjoint cliques will have rank(A) = m < n, and A will be of low rank

Summary

Introduction

With advances in technology and mathematical theory increasingly facilitating the study of complex networks, recent experimental evidence suggests that many networks are more densely-connected than previously proposed. For low values of p, which correspond to more regular networks, the large number of near-lattice connections in A produce a high-rank L and the very few rewires yield a highly sparse S. According to our SL characterization, only for intermediate values of p do we observe unique topological features typically exhibited by densely-connected natural networks, such as the macaque cerebral cortex.

Results

Conclusion