105,466 research outputs found
Evolution of the social network of scientific collaborations
The co-authorship network of scientists represents a prototype of complex
evolving networks.
By mapping the electronic database containing all relevant journals in
mathematics and neuro-science for an eight-year period (1991-98), we infer the
dynamic and the structural mechanisms that govern the evolution and topology of
this complex system.
First, empirical measurements allow us to uncover the topological measures
that characterize the network at a given moment, as well as the time evolution
of these quantities.
The results indicate that the network is scale-free, and that the network
evolution is governed by preferential attachment, affecting both internal and
external links.
However, in contrast with most model predictions the average degree increases
in time, and the node separation decreases.
Second, we propose a simple model that captures the network's time evolution.
Third, numerical simulations are used to uncover the behavior of quantities
that could not be predicted analytically.Comment: 14 pages, 15 figure
Error and attack tolerance of complex networks
Many complex systems, such as communication networks, display a surprising
degree of robustness: while key components regularly malfunction, local
failures rarely lead to the loss of the global information-carrying ability of
the network. The stability of these complex systems is often attributed to the
redundant wiring of the functional web defined by the systems' components. In
this paper we demonstrate that error tolerance is not shared by all redundant
systems, but it is displayed only by a class of inhomogeneously wired networks,
called scale-free networks. We find that scale-free networks, describing a
number of systems, such as the World Wide Web, Internet, social networks or a
cell, display an unexpected degree of robustness, the ability of their nodes to
communicate being unaffected by even unrealistically high failure rates.
However, error tolerance comes at a high price: these networks are extremely
vulnerable to attacks, i.e. to the selection and removal of a few nodes that
play the most important role in assuring the network's connectivity.Comment: 14 pages, 4 figures, Late
The Economics of Small Worlds
We examine a simple economic model of network formation where agents benefit from indirect relationships. We show that small-world featuresâshort path lengths between nodes together with highly clustered link structuresânecessarily emerge for a wide set of parameters
Generalizing Kronecker graphs in order to model searchable networks
This paper describes an extension to stochastic
Kronecker graphs that provides the special structure required
for searchability, by defining a âdistanceâ-dependent Kronecker
operator. We show how this extension of Kronecker graphs
can generate several existing social network models, such as
the Watts-Strogatz small-world model and Kleinbergâs latticebased
model. We focus on a specific example of an expanding
hypercube, reminiscent of recently proposed social network
models based on a hidden hyperbolic metric space, and prove
that a greedy forwarding algorithm can find very short paths
of length O((log log n)^2) for graphs with n nodes
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