Evolving graphs: dynamical models, inverse problems and propagation

Peter Grindrod, D.J. Higham

Research output: Contribution to journalArticle

53 Citations (Scopus)
125 Downloads (Pure)

Abstract

Applications such as neuroscience, telecommunication, on-line social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a realistic but tractable framework for modeling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots, and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.
Original languageEnglish
Pages (from-to)753-770
Number of pages18
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume466
Issue number2115
DOIs
Publication statusPublished - 8 Mar 2010

    Fingerprint

Keywords

  • birth and death process
  • epidemiology
  • network
  • neuroscience
  • random graph
  • reproduction rate

Cite this