10,305 research outputs found
Structural efficiency of percolation landscapes in flow networks
Complex networks characterized by global transport processes rely on the
presence of directed paths from input to output nodes and edges, which organize
in characteristic linked components. The analysis of such network-spanning
structures in the framework of percolation theory, and in particular the key
role of edge interfaces bridging the communication between core and periphery,
allow us to shed light on the structural properties of real and theoretical
flow networks, and to define criteria and quantities to characterize their
efficiency at the interplay between structure and functionality. In particular,
it is possible to assess that an optimal flow network should look like a "hairy
ball", so to minimize bottleneck effects and the sensitivity to failures.
Moreover, the thorough analysis of two real networks, the Internet
customer-provider set of relationships at the autonomous system level and the
nervous system of the worm Caenorhabditis elegans --that have been shaped by
very different dynamics and in very different time-scales--, reveals that
whereas biological evolution has selected a structure close to the optimal
layout, market competition does not necessarily tend toward the most customer
efficient architecture.Comment: 8 pages, 5 figure
Evolution of networks
We review the recent fast progress in statistical physics of evolving
networks. Interest has focused mainly on the structural properties of random
complex networks in communications, biology, social sciences and economics. A
number of giant artificial networks of such a kind came into existence
recently. This opens a wide field for the study of their topology, evolution,
and complex processes occurring in them. Such networks possess a rich set of
scaling properties. A number of them are scale-free and show striking
resilience against random breakdowns. In spite of large sizes of these
networks, the distances between most their vertices are short -- a feature
known as the ``small-world'' effect. We discuss how growing networks
self-organize into scale-free structures and the role of the mechanism of
preferential linking. We consider the topological and structural properties of
evolving networks, and percolation in these networks. We present a number of
models demonstrating the main features of evolving networks and discuss current
approaches for their simulation and analytical study. Applications of the
general results to particular networks in Nature are discussed. We demonstrate
the generic connections of the network growth processes with the general
problems of non-equilibrium physics, econophysics, evolutionary biology, etc.Comment: 67 pages, updated, revised, and extended version of review, submitted
to Adv. Phy
Limited path percolation in complex networks
We study the stability of network communication after removal of
links under the assumption that communication is effective only if the shortest
path between nodes and after removal is shorter than where is the shortest path before removal. For a large
class of networks, we find a new percolation transition at
, where and
is the node degree. Below , only a fraction of
the network nodes can communicate, where , while above , order nodes can
communicate within the limited path length . Our analytical results
are supported by simulations on Erd\H{o}s-R\'{e}nyi and scale-free network
models. We expect our results to influence the design of networks, routing
algorithms, and immunization strategies, where short paths are most relevant.Comment: 11 pages, 3 figures, 1 tabl
Resilience of the Internet to random breakdowns
A common property of many large networks, including the Internet, is that the
connectivity of the various nodes follows a scale-free power-law distribution,
P(k)=ck^-a. We study the stability of such networks with respect to crashes,
such as random removal of sites. Our approach, based on percolation theory,
leads to a general condition for the critical fraction of nodes, p_c, that need
to be removed before the network disintegrates. We show that for a<=3 the
transition never takes place, unless the network is finite. In the special case
of the Internet (a=2.5), we find that it is impressively robust, where p_c is
approximately 0.99.Comment: latex, 3 pages, 1 figure (eps), explanations added, Phys. Rev. Lett.,
in pres
Spectral transitions in networks
We study the level spacing distribution p(s) in the spectrum of random
networks. According to our numerical results, the shape of p(s) in the
Erdos-Renyi (E-R) random graph is determined by the average degree , and
p(s) undergoes a dramatic change when is varied around the critical point
of the percolation transition, =1. When > 1, the p(s) is described by
the statistics of the Gaussian Orthogonal Ensemble (GOE), one of the major
statistical ensembles in Random Matrix Theory, whereas at =1 it follows the
Poisson level spacing distribution. Closely above the critical point, p(s) can
be described in terms of an intermediate distribution between Poisson and the
GOE, the Brody-distribution. Furthermore, below the critical point p(s) can be
given with the help of the regularised Gamma-function. Motivated by these
results, we analyse the behaviour of p(s) in real networks such as the
Internet, a word association network and a protein protein interaction network
as well. When the giant component of these networks is destroyed in a node
deletion process simulating the networks subjected to intentional attack, their
level spacing distribution undergoes a similar transition to that of the E-R
graph.Comment: 11 pages, 5 figure
Width of percolation transition in complex networks
It is known that the critical probability for the percolation transition is
not a sharp threshold, actually it is a region of non-zero width
for systems of finite size. Here we present evidence that for complex networks
, where is the average
length of the percolation cluster, and is the number of nodes in the
network. For Erd\H{o}s-R\'enyi (ER) graphs , while for
scale-free (SF) networks with a degree distribution
and , . We show analytically
and numerically that the \textit{survivability} , which is the
probability of a cluster to survive chemical shells at probability ,
behaves near criticality as . Thus
for probabilities inside the region the behavior of the
system is indistinguishable from that of the critical point
Effectiveness of dismantling strategies on moderated vs. unmoderated online social platforms
Online social networks are the perfect test bed to better understand
large-scale human behavior in interacting contexts. Although they are broadly
used and studied, little is known about how their terms of service and posting
rules affect the way users interact and information spreads. Acknowledging the
relation between network connectivity and functionality, we compare the
robustness of two different online social platforms, Twitter and Gab, with
respect to dismantling strategies based on the recursive censor of users
characterized by social prominence (degree) or intensity of inflammatory
content (sentiment). We find that the moderated (Twitter) vs unmoderated (Gab)
character of the network is not a discriminating factor for intervention
effectiveness. We find, however, that more complex strategies based upon the
combination of topological and content features may be effective for network
dismantling. Our results provide useful indications to design better strategies
for countervailing the production and dissemination of anti-social content in
online social platforms
Overlapping modularity at the critical point of k-clique percolation
One of the most remarkable social phenomena is the formation of communities
in social networks corresponding to families, friendship circles, work teams,
etc. Since people usually belong to several different communities at the same
time, the induced overlaps result in an extremely complicated web of the
communities themselves. Thus, uncovering the intricate community structure of
social networks is a non-trivial task with great potential for practical
applications, gaining a notable interest in the recent years. The Clique
Percolation Method (CPM) is one of the earliest overlapping community finding
methods, which was already used in the analysis of several different social
networks. In this approach the communities correspond to k-clique percolation
clusters, and the general heuristic for setting the parameters of the method is
to tune the system just below the critical point of k-clique percolation.
However, this rule is based on simple physical principles and its validity was
never subject to quantitative analysis. Here we examine the quality of the
partitioning in the vicinity of the critical point using recently introduced
overlapping modularity measures. According to our results on real social- and
other networks, the overlapping modularities show a maximum close to the
critical point, justifying the original criteria for the optimal parameter
settings.Comment: 20 pages, 6 figure
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