34,827 research outputs found
Characterizing the structure of small-world networks
We give exact relations which are valid for small-world networks (SWN's) with
a general `degree distribution', i.e the distribution of nearest-neighbor
connections. For the original SWN model, we illustrate how these exact
relations can be used to obtain approximations for the corresponding basic
probability distribution. In the limit of large system sizes and small
disorder, we use numerical studies to obtain a functional fit for this
distribution. Finally, we obtain the scaling properties for the mean-square
displacement of a random walker, which are determined by the scaling behavior
of the underlying SWN
Clustering and preferential attachment in growing networks
We study empirically the time evolution of scientific collaboration networks
in physics and biology. In these networks, two scientists are considered
connected if they have coauthored one or more papers together. We show that the
probability of scientists collaborating increases with the number of other
collaborators they have in common, and that the probability of a particular
scientist acquiring new collaborators increases with the number of his or her
past collaborators. These results provide experimental evidence in favor of
previously conjectured mechanisms for clustering and power-law degree
distributions in networks.Comment: 13 pages, 2 figure
Small-World Networks: Links with long-tailed distributions
Small-world networks (SWN), obtained by randomly adding to a regular
structure additional links (AL), are of current interest. In this article we
explore (based on physical models) a new variant of SWN, in which the
probability of realizing an AL depends on the chemical distance between the
connected sites. We assume a power-law probability distribution and study
random walkers on the network, focussing especially on their probability of
being at the origin. We connect the results to L\'evy Flights, which follow
from a mean field variant of our model.Comment: 11 pages, 4 figures, to appear in Phys.Rev.
Statistics of Certain Models of Evolution
In a recent paper, Newman surveys the literature on power law spectra in
evolution, self-organised criticality and presents a model of his own to arrive
at a conclusion that self-organised criticality is not necessary for evolution.
Not only did he miss a key model (Ecolab) that has a clear self-organised
critical mechanism, but also Newman's model exhibits the same mechanism that
gives rise to power law behaviour as does Ecolab. Newman's model is, in fact, a
``mean field'' approximation of a self-organised critical system. In this
paper, I have also implemented Newman's model using the Ecolab software,
removing the restriction that the number of species remains constant. It turns
out that the requirement of constant species number is non-trivial, leading to
a global coupling between species that is similar in effect to the species
interactions seen in Ecolab. In fact, the model must self-organise to a state
where the long time average of speciations balances that of the extinctions,
otherwise the system either collapses or explodes. In view of this, Newman's
model does not provide the hoped-for counter example to the presence of
self-organised criticality in evolution, but does provide a simple, almost
analytic model that can used to understand more intricate models such as
Ecolab.Comment: accepted in Phys Rev E.; RevTeX; See
http://parallel.hpc.unsw.edu.au/rks/ecolab.html for more informatio
A dual modelling of evolving political opinion networks
We present the result of a dual modeling of opinion network. The model
complements the agent-based opinion models by attaching to the social agent
(voters) network a political opinion (party) network having its own intrinsic
mechanisms of evolution. These two sub-networks form a global network which can
be either isolated from or dependent on the external influence. Basically, the
evolution of the agent network includes link adding and deleting, the opinion
changes influenced by social validation, the political climate, the
attractivity of the parties and the interaction between them. The opinion
network is initially composed of numerous nodes representing opinions or
parties which are located on a one dimensional axis according to their
political positions. The mechanism of evolution includes union, splitting,
change of position and of attractivity, taken into account the pairwise node
interaction decaying with node distance in power law. The global evolution ends
in a stable distribution of the social agents over a quasi-stable and
fluctuating stationary number of remaining parties. Empirical study on the
lifetime distribution of numerous parties and vote results is carried out to
verify numerical results
Noise-induced volatility of collective dynamics
"Noise-induced volatility" refers to a phenomenon of increased level of
fluctuations in the collective dynamics of bistable units in the presence of a
rapidly varying external signal, and intermediate noise levels. The
archetypical signature of this phenomenon is that --beyond the increase in the
level of fluctuations-- the response of the system becomes uncorrelated with
the external driving force, making it different from stochastic resonance.
Numerical simulations and an analytical theory of a stochastic dynamical
version of the Ising model on regular and random networks demonstrate the
ubiquity and robustness of this phenomenon, which is argued to be a possible
cause of excess volatility in financial markets, of enhanced effective
temperatures in a variety of out-of-equilibrium systems and of strong selective
responses of immune systems of complex biological organisms. Extensive
numerical simulations are compared with a mean-field theory for different
network topologies
Graph Metrics for Temporal Networks
Temporal networks, i.e., networks in which the interactions among a set of
elementary units change over time, can be modelled in terms of time-varying
graphs, which are time-ordered sequences of graphs over a set of nodes. In such
graphs, the concepts of node adjacency and reachability crucially depend on the
exact temporal ordering of the links. Consequently, all the concepts and
metrics proposed and used for the characterisation of static complex networks
have to be redefined or appropriately extended to time-varying graphs, in order
to take into account the effects of time ordering on causality. In this chapter
we discuss how to represent temporal networks and we review the definitions of
walks, paths, connectedness and connected components valid for graphs in which
the links fluctuate over time. We then focus on temporal node-node distance,
and we discuss how to characterise link persistence and the temporal
small-world behaviour in this class of networks. Finally, we discuss the
extension of classic centrality measures, including closeness, betweenness and
spectral centrality, to the case of time-varying graphs, and we review the work
on temporal motifs analysis and the definition of modularity for temporal
graphs.Comment: 26 pages, 5 figures, Chapter in Temporal Networks (Petter Holme and
Jari Saram\"aki editors). Springer. Berlin, Heidelberg 201
Signatures of currency vertices
Many real-world networks have broad degree distributions. For some systems,
this means that the functional significance of the vertices is also broadly
distributed, in other cases the vertices are equally significant, but in
different ways. One example of the latter case is metabolic networks, where the
high-degree vertices -- the currency metabolites -- supply the molecular groups
to the low-degree metabolites, and the latter are responsible for the
higher-order biological function, of vital importance to the organism. In this
paper, we propose a generalization of currency metabolites to currency
vertices. We investigate the network structural characteristics of such
systems, both in model networks and in some empirical systems. In addition to
metabolic networks, we find that a network of music collaborations and a
network of e-mail exchange could be described by a division of the vertices
into currency vertices and others.Comment: to appear in Journal of the Physical Society of Japa
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