Multiscale dynamical embeddings of complex networks

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Title: Multiscale dynamical embeddings of complex networks
Authors: Schaub, MT
Delvenne, JC
Lambiotte, R
Barahona, M
Item Type: Journal Article
Abstract: Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict, and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from control theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i) dimensionality reduction, i.e., projecting nodes onto a low-dimensional space that captures dynamic similarity at different timescales, and (ii) how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to control theory, by using the here developed dynamical perspective.
Issue Date: 20-Jun-2019
Date of Acceptance: 1-Jun-2019
URI: http://hdl.handle.net/10044/1/71570
DOI: https://doi.org/10.1103/PhysRevE.99.062308
ISSN: 1539-3755
Publisher: American Physical Society
Start Page: 062308-1
End Page: 062308-18
Journal / Book Title: Physical Review E
Volume: 99
Issue: 6
Copyright Statement: ©2019 American Physical Society.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/I017267/1
EP/I032223/1
EP/N014529/1
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics, Mathematical
Physics
STOCHASTIC BLOCKMODELS
RANDOM-WALKS
GRAPH
REDUCTION
PREDICTION
SYSTEMS
MAPS
cs.SI
cs.SI
cs.SY
physics.soc-ph
Publication Status: Published
Online Publication Date: 2019-06-09
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics



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