Topological Strata of Weighted Complex Networks
Giovanni Petri,
Martina Scolamiero,
Irene Donato and
Francesco Vaccarino
PLOS ONE, 2013, vol. 8, issue 6, 1-8
Abstract:
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally defined quantities of nodes and edges, such as node degrees, edge weights and –more recently– correlations between neighboring nodes. However, statistical methods quickly become cumbersome when dealing with many-body properties and do not capture the precise mesoscopic structure of complex networks. Here we introduce a novel method, based on persistent homology, to detect particular non-local structures, akin to weighted holes within the link-weight network fabric, which are invisible to existing methods. Their properties divide weighted networks in two broad classes: one is characterized by small hierarchically nested holes, while the second displays larger and longer living inhomogeneities. These classes cannot be reduced to known local or quasilocal network properties, because of the intrinsic non-locality of homological properties, and thus yield a new classification built on high order coordination patterns. Our results show that topology can provide novel insights relevant for many-body interactions in social and spatial networks. Moreover, this new method creates the first bridge between network theory and algebraic topology, which will allow to import the toolset of algebraic methods to complex systems.
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)
Downloads: (external link)
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0066506 (text/html)
https://journals.plos.org/plosone/article/file?id= ... 66506&type=printable (application/pdf)
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0066506
DOI: 10.1371/journal.pone.0066506
Access Statistics for this article
More articles in PLOS ONE from Public Library of Science
Bibliographic data for series maintained by plosone ().