Object-Based Dynamics: Applying Forman–Ricci Flow on a Multigraph to Assess the Impact of an Object on The Network Structure

Haim Cohen, Yinon Nachshon, Anat Maril, Paz M. Naim, Jürgen Jost, Emil Saucan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Temporal information plays a central role in shaping the structure of a network. In this paper, we consider the impact of an object on network structure over time. More specifically, we use a novel object-based dynamic measure to reflect the extent to which an object that is represented in the network by a vertex affects the topology of the network over time. By way of multigraph and Forman–Ricci flow, we assess the object’s impact on graph weights by comparing two graphs, one in which the object is present and one in which the object is absent. After using a case study to demonstrate the impact of Forman–Ricci flow on the network structure, we apply our measure in a semantic network to assess the effects of a word on the interactions between other words that follow it. In addition, we compare our novel measure to centrality and curvature measures so that we can ascertain the advantages of our measure over ones that already exist.

Original languageAmerican English
Article number486
JournalAxioms
Volume11
Issue number9
DOIs
StatePublished - Sep 2022

Bibliographical note

Publisher Copyright:
© 2022 by the authors.

Keywords

  • Forman–Ricci curvature
  • Ricci flow
  • complex network
  • multigraph
  • semantic network

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