437 research outputs found
La Geometria oculta d'Internet
Internet està provocant una revolució tecnològica només comparable amb el desenvolupament de l'electricitat a fi nals
del segle ������. Contràriament al que es pot pensar, Internet no és un sistema planifi cat, sinó que evoluciona de manera
autoorganitzada segons les seves pròpies lleis. Resulta fonamental, doncs, si en volem preveure l'evolució i prevenir possibles
col·lapses del sistema, apropar-nos al seu estudi amb els ulls d'un cien�� fi c. En aquest sen�� t, el protocol més fonamental
d'Internet, l'encarregat de redirigir els paquets d'informació, està pa�� nt una sobrecàrrega deguda al creixement desmesurat
de la xarxa. En aquest ar�� cle presentem una alterna�� va basada en les propietats dels espais hiperbòlics que té el potencial
de conver�� r-se en una alterna�� va viable al protocol actual
Self-similarity of complex networks and hidden metric spaces
We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization
Low-temperature behaviour of social and economic networks
Real-world social and economic networks typically display a number of
particular topological properties, such as a giant connected component, a broad
degree distribution, the small-world property and the presence of communities
of densely interconnected nodes. Several models, including ensembles of
networks also known in social science as Exponential Random Graphs, have been
proposed with the aim of reproducing each of these properties in isolation.
Here we define a generalized ensemble of graphs by introducing the concept of
graph temperature, controlling the degree of topological optimization of a
network. We consider the temperature-dependent version of both existing and
novel models and show that all the aforementioned topological properties can be
simultaneously understood as the natural outcomes of an optimized,
low-temperature topology. We also show that seemingly different graph models,
as well as techniques used to extract information from real networks, are all
found to be particular low-temperature cases of the same generalized formalism.
One such technique allows us to extend our approach to real weighted networks.
Our results suggest that a low graph temperature might be an ubiquitous
property of real socio-economic networks, placing conditions on the diffusion
of information across these systems
Clustering in complex networks. I. General formalism
We develop a full theoretical approach to clustering in complex networks. A
key concept is introduced, the edge multiplicity, that measures the number of
triangles passing through an edge. This quantity extends the clustering
coefficient in that it involves the properties of two --and not just one--
vertices. The formalism is completed with the definition of a three-vertex
correlation function, which is the fundamental quantity describing the
properties of clustered networks. The formalism suggests new metrics that are
able to thoroughly characterize transitive relations. A rigorous analysis of
several real networks, which makes use of the new formalism and the new
metrics, is also provided. It is also found that clustered networks can be
classified into two main groups: the {\it weak} and the {\it strong
transitivity} classes. In the first class, edge multiplicity is small, with
triangles being disjoint. In the second class, edge multiplicity is high and so
triangles share many edges. As we shall see in the following paper, the class a
network belongs to has strong implications in its percolation properties
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