Coarse-graining Directed Networks with Ergodic Sets Preserving Diffusive Dynamics
Apr 11, 2021·
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0 min read
Marco Leonetti
Dr. Erik Hormann
Luca Leuzzi
Giorgio Parisi
Giancarlo Ruocco
Cozzarelli Prize
Abstract
In this paper, we introduce ergodic sets, subsets of nodes of the networks that are dynamically disjoint from the rest of the network (i.e. that can never be reached or left following to the network dynamics). We connect their definition to purely structural considerations of the network and study some of their basic properties. We study numerically the presence of such structures in a number of synthetic network models and in classes of networks from a variety of real-world applications, and we use them to present a compression algorithm that preserve the random walk diffusive dynamics of the original network.
Type
Publication
Proceedings of the National Academy of Sciences of the United States of America
Status
Peer-reviewed
Open access
Awards
Cozzarelli Prize
PNAS · 2021
Best paper, Class III: Engineering and Applied Sciences
Authors
Dr. Erik Hormann
(he/him)
Lecturer in Mathematics
I am a Lecturer in Mathematics at James Cook University Singapore.
My research focuses on network science, stochastic processes, and
statistical mechanics, with particular interests in random walks on
complex networks, network dynamics, and network coarse-graining.
I am also interested in mathematical education and the development
of new approaches to university mathematics assessment.