133 research outputs found
Reliability of rank order in sampled networks
In complex scale-free networks, ranking the individual nodes based upon their
importance has useful applications, such as the identification of hubs for
epidemic control, or bottlenecks for controlling traffic congestion. However,
in most real situations, only limited sub-structures of entire networks are
available, and therefore the reliability of the order relationships in sampled
networks requires investigation. With a set of randomly sampled nodes from the
underlying original networks, we rank individual nodes by three centrality
measures: degree, betweenness, and closeness. The higher-ranking nodes from the
sampled networks provide a relatively better characterisation of their ranks in
the original networks than the lower-ranking nodes. A closeness-based order
relationship is more reliable than any other quantity, due to the global nature
of the closeness measure. In addition, we show that if access to hubs is
limited during the sampling process, an increase in the sampling fraction can
in fact decrease the sampling accuracy. Finally, an estimation method for
assessing sampling accuracy is suggested
Mean-field theory for scale-free random networks
Random networks with complex topology are common in Nature, describing
systems as diverse as the world wide web or social and business networks.
Recently, it has been demonstrated that most large networks for which
topological information is available display scale-free features. Here we study
the scaling properties of the recently introduced scale-free model, that can
account for the observed power-law distribution of the connectivities. We
develop a mean-field method to predict the growth dynamics of the individual
vertices, and use this to calculate analytically the connectivity distribution
and the scaling exponents. The mean-field method can be used to address the
properties of two variants of the scale-free model, that do not display
power-law scaling.Comment: 19 pages, 6 figure
Inhomogeneous substructures hidden in random networks
We study the structure of the load-based spanning tree (LST) that carries the
maximum weight of the Erdos-Renyi (ER) random network. The weight of an edge is
given by the edge-betweenness centrality, the effective number of shortest
paths through the edge. We find that the LSTs present very inhomogeneous
structures in contrast to the homogeneous structures of the original networks.
Moreover, it turns out that the structure of the LST changes dramatically as
the edge density of an ER network increases, from scale free with a cutoff,
scale free, to a starlike topology. These would not be possible if the weights
are randomly distributed, which implies that topology of the shortest path is
correlated in spite of the homogeneous topology of the random network.Comment: 4 pages, 4 figure
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