73,883 research outputs found
Randomness and Complexity in Networks
I start by reviewing some basic properties of random graphs. I then consider
the role of random walks in complex networks and show how they may be used to
explain why so many long tailed distributions are found in real data sets. The
key idea is that in many cases the process involves copying of properties of
near neighbours in the network and this is a type of short random walk which in
turn produce a natural preferential attachment mechanism. Applying this to
networks of fixed size I show that copying and innovation are processes with
special mathematical properties which include the ability to solve a simple
model exactly for any parameter values and at any time. I finish by looking at
variations of this basic model.Comment: Survey paper based on talk given at the workshop on ``Stochastic
Networks and Internet Technology'', Centro di Ricerca Matematica Ennio De
Giorgi, Matematica nelle Scienze Naturali e Sociali, Pisa, 17th - 21st
September 2007. To appear in proceeding
Exact Solutions for Network Rewiring Models
Evolving networks with a constant number of edges may be modelled using a
rewiring process. These models are used to describe many real-world processes
including the evolution of cultural artifacts such as family names, the
evolution of gene variations, and the popularity of strategies in simple
econophysics models such as the minority game. The model is closely related to
Urn models used for glasses, quantum gravity and wealth distributions. The full
mean field equation for the degree distribution is found and its exact solution
and generating solution are given.Comment: 7 pages, 7 figures. Minor changes and corrections made for
publicatio
Thermal Bosonic Green Functions Near Zero Energy (6 characters removed for email)
The properties of the various types of bosonic Green functions at finite
temperature in the zero energy limit are considered in the light of recent
work.Comment: 14, LaTeX (article style), Imperial/TP/91-92/3
Complex Networks
An outline of recent work on complex networks is given from the point of view
of a physicist. Motivation, achievements and goals are discussed with some of
the typical applications from a wide range of academic fields. An introduction
to the relevant literature and useful resources is also given.Comment: Review for Contemporary Physics, 31 page
Thermal Bubble Diagrams Near Zero Energy
The zero four-momentum and equal mass limits are taken for the bubble diagram
of scalar fields. It is seen that RTF and ITF are in complete agreement.
However contributions from this diagram to both retarded and time-ordered
functions do depend on the order of the limits and can be infinite in some
cases. This shows explicitly that the relation between the free energy and a
derivative expansion of a thermal effective action is generally much more
complicated that is the case at zero temperature.Comment: 13 pages, LaTeX (3 PS figures appended), Imperial/TP/92-93/4
Clique Graphs and Overlapping Communities
It is shown how to construct a clique graph in which properties of cliques of
a fixed order in a given graph are represented by vertices in a weighted graph.
Various definitions and motivations for these weights are given. The detection
of communities or clusters is used to illustrate how a clique graph may be
exploited. In particular a benchmark network is shown where clique graphs find
the overlapping communities accurately while vertex partition methods fail.Comment: 23 pages plus 16 additional pages in appendice
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