53,626 research outputs found
Deterministic Small-World Networks
Many real life networks, such as the World Wide Web, transportation systems,
biological or social networks, achieve both a strong local clustering (nodes
have many mutual neighbors) and a small diameter (maximum distance between any
two nodes). These networks have been characterized as small-world networks and
modeled by the addition of randomness to regular structures. We show that
small-world networks can be constructed in a deterministic way. This exact
approach permits a direct calculation of relevant network parameters allowing
their immediate contrast with real-world networks and avoiding complex computer
simulations.Comment: 6 pages, 1 figur
Self-similar planar graphs as models for complex networks
In this paper we introduce a family of planar, modular and self-similar
graphs which have small-world and scale-free properties. The main parameters of
this family are comparable to those of networks associated to complex systems,
and therefore the graphs are of interest as mathematical models for these
systems. As the clustering coefficient of the graphs is zero, this family is an
explicit construction that does not match the usual characterization of
hierarchical modular networks, namely that vertices have clustering values
inversely proportional to their degrees.Comment: 10 pages, submitted to 19th International Workshop on Combinatorial
Algorithms (IWOCA 2008
Polchinski equation, reparameterization invariance and the derivative expansion
The connection between the anomalous dimension and some invariance properties
of the fixed point actions within exact RG is explored. As an application,
Polchinski equation at next-to-leading order in the derivative expansion is
studied. For the Wilson fixed point of the one-component scalar theory in three
dimensions we obtain the critical exponents \eta=0.042, \nu=0.622 and
\omega=0.754.Comment: 28 pages, LaTeX with psfig, 12 encapsulated PostScript figures. A
number wrongly quoted in the abstract correcte
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