Spectral analysis on explosive percolation

¹ Temasek Laboratories, National University of Singapore - Singapore 117508
² Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University - 21 Nanyang Links, Singapore 637371
³ Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Singapore), National University of Singapore - Kent Ridge 119260, Singapore
⁴ Department of Physics, National University of Singapore - Singapore 117542
⁵ Yale-NUS College - 6 College Avenue East, Singapore 138614

Received: 6 January 2013
Accepted: 4 March 2013

Abstract

We study the spectral properties of the process of explosive percolation. In particular, we explore how the maximum eigenvalue of the adjacency matrix of a network which governs the spreading efficiency evolves as the density of connection increases. Interestingly, for networks with connectivity that grow in an explosive way, information spreading and mass transport are found to be carried out inefficiently. In the conventional explosive percolation models that we studied, the sudden emergences of large-scale connectivity are found to come with relatively lowered efficiency of spreading. Nevertheless, the spreading efficiency of the explosive model can be increased by introducing heterogeneous structures into the networks.