527,860 research outputs found
Empirical study on clique-degree distribution of networks
The community structure and motif-modular-network hierarchy are of great
importance for understanding the relationship between structures and functions.
In this paper, we investigate the distribution of clique-degree, which is an
extension of degree and can be used to measure the density of cliques in
networks. The empirical studies indicate the extensive existence of power-law
clique-degree distributions in various real networks, and the power-law
exponent decreases with the increasing of clique size.Comment: 9 figures, 4 page
Two universal physical principles shape the power-law statistics of real-world networks
The study of complex networks has pursued an understanding of macroscopic
behavior by focusing on power-laws in microscopic observables. Here, we uncover
two universal fundamental physical principles that are at the basis of complex
networks generation. These principles together predict the generic emergence of
deviations from ideal power laws, which were previously discussed away by
reference to the thermodynamic limit. Our approach proposes a paradigm shift in
the physics of complex networks, toward the use of power-law deviations to
infer meso-scale structure from macroscopic observations.Comment: 14 pages, 7 figure
Planar unclustered scale-free graphs as models for technological and biological networks
Many real life networks present an average path length logarithmic with the
number of nodes and a degree distribution which follows a power law. Often
these networks have also a modular and self-similar structure and, in some
cases - usually associated with topological restrictions- their clustering is
low and they are almost planar. In this paper we introduce a family of graphs
which share all these properties and are defined by two parameters. As their
construction is deterministic, we obtain exact analytic expressions for
relevant properties of the graphs including the degree distribution, degree
correlation, diameter, and average distance, as a function of the two defining
parameters. Thus, the graphs are useful to model some complex networks, in
particular several families of technological and biological networks, and in
the design of new practical communication algorithms in relation to their
dynamical processes. They can also help understanding the underlying mechanisms
that have produced their particular structure.Comment: Accepted for publication in Physica
Social encounter networks : collective properties and disease transmission
A fundamental challenge of modern infectious disease epidemiology is to quantify the networks of social and physical contacts through which transmission can occur. Understanding the collective properties of these interactions is critical for both accurate prediction of the spread of infection and determining optimal control measures. However, even the basic properties of such networks are poorly quantified, forcing predictions to be made based on strong assumptions concerning network structure. Here, we report on the results of a large-scale survey of social encounters mainly conducted in Great Britain. First, we characterize the distribution of contacts, which possesses a lognormal body and a power-law tail with an exponent of −2.45; we provide a plausible mechanistic model that captures this form. Analysis of the high level of local clustering of contacts reveals additional structure within the network, implying that social contacts are degree assortative. Finally, we describe the epidemiological implications of this local network structure: these contradict the usual predictions from networks with heavy-tailed degree distributions and contain public-health messages about control. Our findings help us to determine the types of realistic network structure that should be assumed in future population level studies of infection transmission, leading to better interpretations of epidemiological data and more appropriate policy decisions
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