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Mathematical Problems in Engineering
Volume 2013, Article ID 815035, 7 pages
http://dx.doi.org/10.1155/2013/815035
Research Article

Persistent Homology of Collaboration Networks

School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, VIC 3001, Australia

Received 29 March 2013; Accepted 19 May 2013

Academic Editor: Tingwen Huang

Copyright © 2013 C. J. Carstens and K. J. Horadam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Over the past few decades, network science has introduced several statistical measures to determine the topological structure of large networks. Initially, the focus was on binary networks, where edges are either present or not. Thus, many of the earlier measures can only be applied to binary networks and not to weighted networks. More recently, it has been shown that weighted networks have a rich structure, and several generalized measures have been introduced. We use persistent homology, a recent technique from computational topology, to analyse four weighted collaboration networks. We include the first and second Betti numbers for the first time for this type of analysis. We show that persistent homology corresponds to tangible features of the networks. Furthermore, we use it to distinguish the collaboration networks from similar random networks.