81 research outputs found
Weighted Configuration Model
The configuration model is one of the most successful models for generating
uncorrelated random networks. We analyze its behavior when the expected degree
sequence follows a power law with exponent smaller than two. In this situation,
the resulting network can be viewed as a weighted network with non trivial
correlations between strength and degree. Our results are tested against large
scale numerical simulations, finding excellent agreement.Comment: Proceedings CNET200
Percolation in self-similar networks
We provide a simple proof that graphs in a general class of self-similar
networks have zero percolation threshold. The considered self-similar networks
include random scale-free graphs with given expected node degrees and zero
clustering, scale-free graphs with finite clustering and metric structure,
growing scale-free networks, and many real networks. The proof and the
derivation of the giant component size do not require the assumption that
networks are treelike. Our results rely only on the observation that
self-similar networks possess a hierarchy of nested subgraphs whose average
degree grows with their depth in the hierarchy. We conjecture that this
property is pivotal for percolation in networks.Comment: 4 pages, 3 figure
Correlations in weighted networks
We develop a statistical theory to characterize correlations in weighted
networks. We define the appropriate metrics quantifying correlations and show
that strictly uncorrelated weighted networks do not exist due to the presence
of structural constraints. We also introduce an algorithm for generating
maximally random weighted networks with arbitrary to be used as null
models. The application of our measures to real networks reveals the importance
of weights in a correct understanding and modeling of these heterogeneous
systems.Comment: 4 pages, 2 figure
Modeling the Internet
We model the Internet as a network of interconnected Autonomous Systems which
self-organize under an absolute lack of centralized control. Our aim is to
capture how the Internet evolves by reproducing the assembly that has led to
its actual structure and, to this end, we propose a growing weighted network
model driven by competition for resources and adaptation to maintain
functionality in a demand and supply ``equilibrium''. On the demand side, we
consider the environment, a pool of users which need to transfer information
and ask for service. On the supply side, ASs compete to gain users, but to be
able to provide service efficiently, they must adapt their bandwidth as a
function of their size. Hence, the Internet is not modeled as an isolated
system but the environment, in the form of a pool of users, is also a
fundamental part which must be taken into account. ASs compete for users and
big and small come up, so that not all ASs are identical. New connections
between ASs are made or old ones are reinforced according to the adaptation
needs. Thus, the evolution of the Internet can not be fully understood if just
described as a technological isolated system. A socio-economic perspective must
also be considered.Comment: Submitted to the Proceedings of the 3rd International Conference
NEXT-SigmaPh
Extracting the multiscale backbone of complex weighted networks
A large number of complex systems find a natural abstraction in the form of
weighted networks whose nodes represent the elements of the system and the
weighted edges identify the presence of an interaction and its relative
strength. In recent years, the study of an increasing number of large scale
networks has highlighted the statistical heterogeneity of their interaction
pattern, with degree and weight distributions which vary over many orders of
magnitude. These features, along with the large number of elements and links,
make the extraction of the truly relevant connections forming the network's
backbone a very challenging problem. More specifically, coarse-graining
approaches and filtering techniques are at struggle with the multiscale nature
of large scale systems. Here we define a filtering method that offers a
practical procedure to extract the relevant connection backbone in complex
multiscale networks, preserving the edges that represent statistical
significant deviations with respect to a null model for the local assignment of
weights to edges. An important aspect of the method is that it does not
belittle small-scale interactions and operates at all scales defined by the
weight distribution. We apply our method to real world network instances and
compare the obtained results with alternative backbone extraction techniques
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