421 research outputs found
Information mobility in complex networks
The concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network. The transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one. We use the fractional powers of this transition matrix to investigate the stochastic process at fractional time intervals. The mobility coefficient is then introduced on the basis of the trace of these fractional powers of the stochastic matrix. The fractional time at which a network diffuses 50% of the information contained in its nodes (1/ k50 ) is also introduced. We then show that the scale-free random networks display better spread of information than the non scale-free ones. We study 38 real-world networks and analyze their performance in spreading information from their nodes. We find that some real-world networks perform even better than the scale-free networks with the same average degree and we point out some of the structural parameters that make this possible
Corrected overlap weight and clustering coefficient
We discuss two well known network measures: the overlap weight of an edge and
the clustering coefficient of a node. For both of them it turns out that they
are not very useful for data analytic task to identify important elements
(nodes or links) of a given network. The reason for this is that they attain
their largest values on maximal subgraphs of relatively small size that are
more probable to appear in a network than that of larger size. We show how the
definitions of these measures can be corrected in such a way that they give the
expected results. We illustrate the proposed corrected measures by applying
them on the US Airports network using the program Pajek.Comment: The paper is a detailed and extended version of the talk presented at
the CMStatistics (ERCIM) 2015 Conferenc
Avalanches in complex spin networks
We investigate the magnetization reversal processes on classes of complex
spin networks with antiferromagnetic interaction along the network links. With
slow field ramping the hysteresis loop and avalanches of spin flips occur due
to topological inhomogeneity of the network, even without any disorder of the
magnetic interaction [B. Tadic, et al., Phys. Rev. Lett. 94 (2005) 137204].
Here we study in detail properties of the magnetization avalanches, hysteresis
curves and density of domain walls and show how they can be related to the
structural inhomogeneity of the network. The probability distribution of the
avalanche size, N_s(s), displays the power-law behaviour for small s, i.e.
N_s(s)\propto s^{-\alpha}. For the scale-free networks, grown with preferential
attachment, \alpha increases with the connectivity parameter M from 1.38 for
M=1 (trees) to 1.52 for M=25. For the exponential networks, \alpha is close to
1.0 in the whole range of M.Comment: 16 pages, 10 figures in 29 eps file
Resistance distance, information centrality, node vulnerability and vibrations in complex networks
We discuss three seemingly unrelated quantities that have been introduced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability.We argue that the node displacement has a better resolution as a measure of node vulnerability than the degree and the information centrality
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