In this section
@inbook{Schaub:2019:10.1002/9781119483298.ch12,
author = {Schaub, MT and Delvenne, J-C and Lambiotte, R and Barahona, M},
booktitle = {Advances in Network Clustering and Blockmodeling},
doi = {10.1002/9781119483298.ch12},
editor = {Doreian and Batagelj and Ferligoj},
pages = {333--361},
publisher = {John Wiley and Sons, Ltd},
title = {Structured networks and coarse-grained descriptions: a dynamical perspective},
url = {http://dx.doi.org/10.1002/9781119483298.ch12},
year = {2019}
}
TY - CHAP
AB - This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We thus aim to gain a reduced description of the system that takes into account both its structure and dynamics. In the first part, we introduce the general mathematical setup for the types of dynamics we consider throughout the chapter. We provide two guiding examples, namely consensus dynamics and diffusion processes (random walks), motivating their connection to social network analysis, and provide a brief discussion on the general dynamical framework and its possible extensions. In the second part, we focus on the influence of graph structure on the dynamics taking place on the network, focusing on three concepts that allow us to gain insight into this notion. First, we describe how time scale separation can appear in the dynamics on a network as a consequence of graph structure. Second, we discuss how the presence of particular symmetries in the network give rise to invariant dynamical subspaces that can be precisely described by graph partitions. Third, we show how this dynamical viewpoint can be extended to study dynamics on networks with signed edges, which allow us to discuss connections to concepts in social network analysis, such as structural balance. In the third part, we discuss how to use dynamical processes unfolding on the network to detect meaningful network substructures. We then show how such dynamical measures can be related to seemingly different algorithm for community detection and coarse-graining proposed in the literature. We conclude with a brief summary and highlight interesting open future directions.
AU - Schaub,MT
AU - Delvenne,J-C
AU - Lambiotte,R
AU - Barahona,M
DO - 10.1002/9781119483298.ch12
EP - 361
PB - John Wiley and Sons, Ltd
PY - 2019///
SN - 9781119224709
SP - 333
TI - Structured networks and coarse-grained descriptions: a dynamical perspective
T1 - Advances in Network Clustering and Blockmodeling
UR - http://dx.doi.org/10.1002/9781119483298.ch12
UR - http://arxiv.org/abs/1804.06268v1
UR - http://hdl.handle.net/10044/1/76097
ER -