Load distribution in weighted complex networks

Abstract

We study the load distribution in weighted networks by measuring the effective number of optimal paths passing through a given vertex. The optimal path, along which the total cost is minimum, crucially depend on the cost distribution function $p_c(c)$. In the strong disorder limit, where $p_c(c)\sim c^{-1}$, the load distribution follows a power law both in the Erdős-Rényi (ER) random graphs and in the scale-free (SF) networks, and its characteristics are determined by the structure of the minimum spanning tree. The distribution of loads at vertices with a given vertex degree also follows the SF nature similar to the whole load distribution, implying that the global transport property is not correlated to the local structural information. Finally, we measure the effect of disorder by the correlation coefficient between vertex degree and load, finding that it is larger for ER networks than for SF networks.

4 pages, 4 figures, final version published in PRE

References in corpus (16)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• The architecture of complex weighted networks
• Evolution of networks
• Who is the best connected scientist? A study of scientific coauthorship networks
• Universal Behavior of Load Distribution in Scale-free Networks
• Optimal network topologies for local search with congestion
• Percolation Critical Exponents in Scale-Free Networks
• Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations
• Optimal Paths in Disordered Complex Networks
• Hierarchy Measures in Complex Networks
• Information Super-Diffusion on Structured Networks
• Evolution of scale-free random graphs: Potts model formulation
• Stability of shortest paths in complex networks with random edge weights
• Random Walks on Complex Networks

Cited by in corpus (13)

• Power grids vulnerability: a complex network approach
• Transport in weighted networks: Partition into superhighways and roads
• On the universality of the scaling of fluctuations in traffic on complex networks
• Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks
• Optimal Path and Minimal Spanning Trees in Random Weighted Networks
• Synchronization in Weighted Uncorrelated Complex Networks in a Noisy Environment: Optimization and Connections with Transport Efficiency
• Betweenness centrality of teams in social networks
• The Role of Weight on Community Structure of Networks
• Transport on weighted Networks: when correlations are independent of degree
• Optimization of transport protocols with path-length constraints in complex networks
• Phase transitions in Ising model induced by weight redistribution on weighted regular networks
• Weighted networks of scientific communication: the measurement and geometrical role of weight
• Evolving Model of Weighted Networks Inspired by Scientific Collaboration Networks