Advances in Network Clustering and Blockmodeling

12Structured Networks and Coarse-Grained Descriptions: A Dynamical Perspective

Michael T. Schaub^1,2, Jean-Charles Delvenne³, Renaud Lambiotte^4,5, and Mauricio Barahona^6,7

¹Institute for Data, Systems and Society, Massachusetts Institute of Technology

²Department of Engineering Sciences, University of Oxford

³ICTEAM and CORE, Université Catholique de Louvain

⁴Mathematical Institute, University of Oxford

⁵Entités de recherche: Institut Namurois des systémes complexes (naXys) University of Namur

⁶Department of Mathematics, Imperial College London

⁷EPSRC Centre for Mathematics of Precision Healthcare, Imperial College London

12.1 Introduction

The language of networks and graphs has become a ubiquitous tool to formalize and analyze systems and relational data across scientific disciplines, from biology to physics, from computer science to sociology [50]. Accordingly, scholars from a variety of areas have investigated such networks from different angles, developing diverse computational and mathematical toolboxes in order to analyze and ascribe meaning to the different patterns found in specific networks of interest. Modular structures are one of the most commonly studied features of networks in this context [24,25,58,67,74]. Yet, as highlighted by the lack of a common terminology (modules, partitions, blocks, communities, and clusters are but a few terms commonly found to denote various notions of modular structure in the literature), why scholars are interested in modular structures ...