Hidden communities in networks
Employing theoretical measures to detect communities and connections in complex networks.
The devil is in the detail, when it comes to complex networks. Whilst holistic behaviour and evolution can be understood by studying the global properties of a network, many properties are hidden within the substructure. Solving graphs analytically cannot capture the relevant small-scale dynamics, whilst using brute-force numerics is extremely expensive for large networks, if feasible at all.
In this project, novel methods and measures tease out exact solutions for the evolution of hierarchical structures within complex networks. Ideas from information theory, statistical models, and graph theory seek out links and groups quantitatively, enabling community detection and an understanding of how these substructures feed forward to the global behaviour of the network.
Real-world networks, from biological systems to interconnected financial institutions, are systems that thrive or fail due to small-scale effects that propagate. Honing in on the communities and links that drive these networks in a way that doesn’t require unlimited computational resources, will help to optimise and safeguard their evolution.
Naturally occurring networks have an underlying scale-free structure that is often clouded by finite-size effects in the sample data.
An iterative version of a method to identify hierarchies and rankings of nodes in directed networks can partly overcome its resolution limit.
The spectral density of graph ensembles provides an exact solution to the graph partitioning problem and helps detect community structure.
Inference from single snapshots of temporal networks can misleadingly group communities if the links between snapshots are correlated.
A new tool derived from information theory quantitatively identifies trees, hierarchies and community structures within complex networks.