Minimum spanning trees of weighted scale-free networksP. J. Macdonald, E. Almaas and A.-L. Barabási
Center for Network Research and Department of Physics, University of Notre Dame Notre Dame, IN 46556, USA
received 18 July 2005; accepted 26 August 2005
published online 14 September 2005
A complete characterization of real networks requires us to understand the consequences of the uneven interaction strengths between a system's components. Here we use minimum spanning trees (MSTs) to explore the effect of correlations between link weights and network topology on scale-free networks. Solely by changing the nature of the correlations between weights and network topology, the structure of the MSTs can change from scale-free to exponential. Additionally, for some choices of weight correlations, the efficiency of the MSTs increases with increasing network size, a result with potential implications for the design and scalability of communication networks.
89.75.Fb - Structures and organization in complex systems.
89.75.Hc - Networks and genealogical trees.
89.20.Hh - World Wide Web, Internet.
© EDP Sciences 2005