337,514 research outputs found
On the Perturbation of Self-Organized Urban Street Networks
We investigate urban street networks as a whole within the frameworks of
information physics and statistical physics. Urban street networks are
envisaged as evolving social systems subject to a Boltzmann-mesoscopic entropy
conservation. For self-organized urban street networks, our paradigm has
already allowed us to recover the effectively observed scale-free distribution
of roads and to foresee the distribution of junctions. The entropy conservation
is interpreted as the conservation of the surprisal of the city-dwellers for
their urban street network. In view to extend our investigations to other urban
street networks, we consider to perturb our model for self-organized urban
street networks by adding an external surprisal drift. We obtain the statistics
for slightly drifted self-organized urban street networks. Besides being
practical and manageable, this statistics separates the macroscopic evolution
scale parameter from the mesoscopic social parameters. This opens the door to
observational investigations on the universality of the evolution scale
parameter. Ultimately, we argue that the strength of the external surprisal
drift might be an indicator for the disengagement of the city-dwellers for
their city.Comment: 22 pages, 4 figures + 1 table, LaTeX2e+BMCArt+AmSLaTeX+enote
Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)
Although the ``scale-free'' literature is large and growing, it gives neither
a precise definition of scale-free graphs nor rigorous proofs of many of their
claimed properties. In fact, it is easily shown that the existing theory has
many inherent contradictions and verifiably false claims. In this paper, we
propose a new, mathematically precise, and structural definition of the extent
to which a graph is scale-free, and prove a series of results that recover many
of the claimed properties while suggesting the potential for a rich and
interesting theory. With this definition, scale-free (or its opposite,
scale-rich) is closely related to other structural graph properties such as
various notions of self-similarity (or respectively, self-dissimilarity).
Scale-free graphs are also shown to be the likely outcome of random
construction processes, consistent with the heuristic definitions implicit in
existing random graph approaches. Our approach clarifies much of the confusion
surrounding the sensational qualitative claims in the scale-free literature,
and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet
Mathematics (2005
Resource location based on precomputed partial random walks in dynamic networks
The problem of finding a resource residing in a network node (the
\emph{resource location problem}) is a challenge in complex networks due to
aspects as network size, unknown network topology, and network dynamics. The
problem is especially difficult if no requirements on the resource placement
strategy or the network structure are to be imposed, assuming of course that
keeping centralized resource information is not feasible or appropriate. Under
these conditions, random algorithms are useful to search the network. A
possible strategy for static networks, proposed in previous work, uses short
random walks precomputed at each network node as partial walks to construct
longer random walks with associated resource information. In this work, we
adapt the previous mechanisms to dynamic networks, where resource instances may
appear in, and disappear from, network nodes, and the nodes themselves may
leave and join the network, resembling realistic scenarios. We analyze the
resulting resource location mechanisms, providing expressions that accurately
predict average search lengths, which are validated using simulation
experiments. Reduction of average search lengths compared to simple random walk
searches are found to be very large, even in the face of high network
volatility. We also study the cost of the mechanisms, focusing on the overhead
implied by the periodic recomputation of partial walks to refresh the
information on resources, concluding that the proposed mechanisms behave
efficiently and robustly in dynamic networks.Comment: 39 pages, 25 figure
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