81,208 research outputs found
Direct, physically-motivated derivation of the contagion condition for spreading processes on generalized random networks
For a broad range single-seed contagion processes acting on generalized
random networks, we derive a unifying analytic expression for the possibility
of global spreading events in a straightforward, physically intuitive fashion.
Our reasoning lays bare a direct mechanical understanding of an archetypal
spreading phenomena that is not evident in circuitous extant mathematical
approaches.Comment: 4 pages, 1 figure, 1 tabl
Mixing patterns and community structure in networks
Common experience suggests that many networks might possess community
structure - division of vertices into groups, with a higher density of edges
within groups than between them. Here we describe a new computer algorithm that
detects structure of this kind. We apply the algorithm to a number of
real-world networks and show that they do indeed possess non-trivial community
structure. We suggest a possible explanation for this structure in the
mechanism of assortative mixing, which is the preferential association of
network vertices with others that are like them in some way. We show by
simulation that this mechanism can indeed account for community structure. We
also look in detail at one particular example of assortative mixing, namely
mixing by vertex degree, in which vertices with similar degree prefer to be
connected to one another. We propose a measure for mixing of this type which we
apply to a variety of networks, and also discuss the implications for network
structure and the formation of a giant component in assortatively mixed
networks.Comment: 21 pages, 9 postscript figures, 2 table
Structure of Peer-to-Peer Social Networks
This paper presents a statistical analysis of the structure of Peer-to-Peer
(P2P) social networks that captures social associations of distributed peers in
resource sharing. Peer social networks appear to be mainly composed of pure
resource providers that guarantee high resource availability and reliability of
P2P systems. The major peers that both provide and request resources are only a
small fraction. The connectivity between peers, including undirected, directed
(out and in) and weighted connections, is scale-free and the social networks of
all peers and major peers are small world networks. The analysis also confirms
that peer social networks show in general disassortative correlations, except
that active providers are connected between each other and by active
requesters. The study presented in this paper gives a better understanding of
peer relationships in resource sharing, which may help a better design of
future P2P networks and open the path to the study of transport processes on
top of real P2P topologies.Comment: APS Style, 8 pages, 5 figures and 4 tables. Final versio
The structure and function of complex networks
Inspired by empirical studies of networked systems such as the Internet,
social networks, and biological networks, researchers have in recent years
developed a variety of techniques and models to help us understand or predict
the behavior of these systems. Here we review developments in this field,
including such concepts as the small-world effect, degree distributions,
clustering, network correlations, random graph models, models of network growth
and preferential attachment, and dynamical processes taking place on networks.Comment: Review article, 58 pages, 16 figures, 3 tables, 429 references,
published in SIAM Review (2003
A simple person's approach to understanding the contagion condition for spreading processes on generalized random networks
We present derivations of the contagion condition for a range of spreading
mechanisms on families of generalized random networks and bipartite random
networks. We show how the contagion condition can be broken into three
elements, two structural in nature, and the third a meshing of the contagion
process and the network. The contagion conditions we obtain reflect the
spreading dynamics in a clear, interpretable way. For threshold contagion, we
discuss results for all-to-all and random network versions of the model, and
draw connections between them.Comment: 10 pages, 9 figures; chapter to appear in "Spreading Dynamics in
Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur
Exact solutions for social and biological contagion models on mixed directed and undirected, degree-correlated random networks
We derive analytic expressions for the possibility, probability, and expected
size of global spreading events starting from a single infected seed for a
broad collection of contagion processes acting on random networks with both
directed and undirected edges and arbitrary degree-degree correlations. Our
work extends previous theoretical developments for the undirected case, and we
provide numerical support for our findings by investigating an example class of
networks for which we are able to obtain closed-form expressions.Comment: 10 pages, 3 figure
Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus
We study the effects of network topology on the response of networks of
coupled discrete excitable systems to an external stochastic stimulus. We
extend recent results that characterize the response in terms of spectral
properties of the adjacency matrix by allowing distributions in the
transmission delays and in the number of refractory states, and by developing a
nonperturbative approximation to the steady state network response. We confirm
our theoretical results with numerical simulations. We find that the steady
state response amplitude is inversely proportional to the duration of
refractoriness, which reduces the maximum attainable dynamic range. We also
find that transmission delays alter the time required to reach steady state.
Importantly, neither delays nor refractoriness impact the general prediction
that criticality and maximum dynamic range occur when the largest eigenvalue of
the adjacency matrix is unity
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