19,959 research outputs found
On the Mixing Time of Geographical Threshold Graphs
We study the mixing time of random graphs in the -dimensional toric unit
cube generated by the geographical threshold graph (GTG) model, a
generalization of random geometric graphs (RGG). In a GTG, nodes are
distributed in a Euclidean space, and edges are assigned according to a
threshold function involving the distance between nodes as well as randomly
chosen node weights, drawn from some distribution. The connectivity threshold
for GTGs is comparable to that of RGGs, essentially corresponding to a
connectivity radius of . However, the degree distributions
at this threshold are quite different: in an RGG the degrees are essentially
uniform, while RGGs have heterogeneous degrees that depend upon the weight
distribution. Herein, we study the mixing times of random walks on
-dimensional GTGs near the connectivity threshold for . If the
weight distribution function decays with for an arbitrarily small constant then the mixing time
of GTG is \mixbound. This matches the known mixing bounds for the
-dimensional RGG
Effects of population mixing on the spread of SIR epidemics
We study dynamics of spread of epidemics of SIR type in a realistic
spatially-explicit geographical region, Southern and Central Ontario, using
census data obtained from Statistics Canada, and examine the role of population
mixing in epidemic processes. Our model incorporates the random nature of
disease transmission, the discreteness and heterogeneity of distribution of
host population. We find that introduction of a long-range interaction destroys
spatial correlations very easily if neighbourhood sizes are homogeneous. For
inhomogeneous neighbourhoods, very strong long-range coupling is required to
achieve a similar effect. Our work applies to the spread of in influenza during
a single season and our model is applicable to other geographic regions, if
suitable data is available
Complex network analysis and nonlinear dynamics
This chapter aims at reviewing complex network and nonlinear dynamical
models and methods that were either developed for or applied to socioeconomic
issues, and pertinent to the theme of New Economic Geography. After an introduction
to the foundations of the field of complex networks, the present summary
introduces some applications of complex networks to economics, finance, epidemic
spreading of innovations, and regional trade and developments. The chapter also
reviews results involving applications of complex networks to other relevant
socioeconomic issue
Ordered community structure in networks
Community structure in networks is often a consequence of homophily, or
assortative mixing, based on some attribute of the vertices. For example,
researchers may be grouped into communities corresponding to their research
topic. This is possible if vertex attributes have discrete values, but many
networks exhibit assortative mixing by some continuous-valued attribute, such
as age or geographical location. In such cases, no discrete communities can be
identified. We consider how the notion of community structure can be
generalized to networks that are based on continuous-valued attributes: in
general, a network may contain discrete communities which are ordered according
to their attribute values. We propose a method of generating synthetic ordered
networks and investigate the effect of ordered community structure on the
spread of infectious diseases. We also show that community detection algorithms
fail to recover community structure in ordered networks, and evaluate an
alternative method using a layout algorithm to recover the ordering.Comment: This is an extended preprint version that includes an extra example:
the college football network as an ordered (spatial) network. Further
improvements, not included here, appear in the journal version. Original
title changed (from "Ordered and continuous community structure in networks")
to match journal versio
Network analysis identifies weak and strong links in a metapopulation system
The identification of key populations shaping the structure and connectivity of metapopulation systems is a major challenge in population ecology. The use of molecular markers in the theoretical framework of population genetics has allowed great advances in this field, but the prime question of quantifying the role of each population in the system remains unresolved. Furthermore, the use and interpretation of classical methods are still bounded by the need for a priori information and underlying assumptions that are seldom respected in natural systems. Network theory was applied to map the genetic structure in a metapopulation system by using microsatellite data from populations of a threatened seagrass, Posidonia oceanica, across its whole geographical range. The network approach, free from a priori assumptions and from the usual underlying hypotheses required for the interpretation of classical analyses, allows both the straightforward characterization of hierarchical population structure and the detection of populations acting as hubs critical for relaying gene flow or sustaining the metapopulation system. This development opens perspectives in ecology and evolution in general, particularly in areas such as conservation biology and epidemiology, where targeting specific populations is crucial
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
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