Modularity and Dynamics on Complex Networks

This Element explores the relations between dynamics and modularity on networks, emphasising the importance of time scale separation and network symmetry.

Renaud Lambiotte (Author), Michael T. Schaub (Author)

9781108733533, Cambridge University Press

Paperback / softback, published 3 February 2022

75 pages
22.9 x 15.2 x 0.6 cm, 0.16 kg

Complex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on networks.

1. Introduction
2. Background Material
3. Modularity, community detection and clustering in networks
4. Time scale separation and dynamics on modular networks
5. Symmetries and dynamics on modular networks
6. Dynamical methods for assortative communities
7. Dynamical methods for disassortative communities and general block structures
8. Perspectives
References.

Subject Areas: Maths for computer scientists [UYAM], Mathematical physics [PHU], Statistical physics [PHS], Discrete mathematics [PBD]