33 research outputs found
Comparison of Failures and Attacks on Random and Scale-Free Networks
It appeared recently that some statistical properties of complex networks like the Internet, the World Wide Web or Peer-to-Peer systems have an important influence on their resilience to failures and attacks. In particular, scale-free networks (i.e. networks with power-law degree distribution) seem much more robust than random networks in case of failures, while they are more sensitive to attacks. In this paper we deepen the study of the differences in the behavior of these two kinds of networks when facing failures or attacks. We moderate the general affirmation that scale-free networks are much more sensitive than random networks to attacks by showing that the number of links to remove in both cases is similar, and by showing that a slightly modified scenario for failures gives results similar to the ones for attacks. We also propose and analyze an efficient attack strategy against links
Percolation in Directed Scale-Free Networks
Many complex networks in nature have directed links, a property that affects
the network's navigability and large-scale topology. Here we study the
percolation properties of such directed scale-free networks with correlated in-
and out-degree distributions. We derive a phase diagram that indicates the
existence of three regimes, determined by the values of the degree exponents.
In the first regime we regain the known directed percolation mean field
exponents. In contrast, the second and third regimes are characterized by
anomalous exponents, which we calculate analytically. In the third regime the
network is resilient to random dilution, i.e., the percolation threshold is
p_c->1.Comment: Latex, 5 pages, 2 fig
Range-based attack on links in scale-free networks: are long-range links responsible for the small-world phenomenon?
The small-world phenomenon in complex networks has been identified as being
due to the presence of long-range links, i.e., links connecting nodes that
would otherwise be separated by a long node-to-node distance. We find,
surprisingly, that many scale-free networks are more sensitive to attacks on
short-range than on long-range links. This result, besides its importance
concerning network efficiency and/or security, has the striking implication
that the small-world property of scale-free networks is mainly due to
short-range links.Comment: 4 pages, 4 figures, Revtex, published versio
Cascade-based attacks on complex networks
We live in a modern world supported by large, complex networks. Examples
range from financial markets to communication and transportation systems. In
many realistic situations the flow of physical quantities in the network, as
characterized by the loads on nodes, is important. We show that for such
networks where loads can redistribute among the nodes, intentional attacks can
lead to a cascade of overload failures, which can in turn cause the entire or a
substantial part of the network to collapse. This is relevant for real-world
networks that possess a highly heterogeneous distribution of loads, such as the
Internet and power grids. We demonstrate that the heterogeneity of these
networks makes them particularly vulnerable to attacks in that a large-scale
cascade may be triggered by disabling a single key node. This brings obvious
concerns on the security of such systems.Comment: 4 pages, 4 figures, Revte
Are randomly grown graphs really random?
We analyze a minimal model of a growing network. At each time step, a new
vertex is added; then, with probability delta, two vertices are chosen
uniformly at random and joined by an undirected edge. This process is repeated
for t time steps. In the limit of large t, the resulting graph displays
surprisingly rich characteristics. In particular, a giant component emerges in
an infinite-order phase transition at delta = 1/8. At the transition, the
average component size jumps discontinuously but remains finite. In contrast, a
static random graph with the same degree distribution exhibits a second-order
phase transition at delta = 1/4, and the average component size diverges there.
These dramatic differences between grown and static random graphs stem from a
positive correlation between the degrees of connected vertices in the grown
graph--older vertices tend to have higher degree, and to link with other
high-degree vertices, merely by virtue of their age. We conclude that grown
graphs, however randomly they are constructed, are fundamentally different from
their static random graph counterparts.Comment: 8 pages, 5 figure
The spread of epidemic disease on networks
The study of social networks, and in particular the spread of disease on
networks, has attracted considerable recent attention in the physics community.
In this paper, we show that a large class of standard epidemiological models,
the so-called susceptible/infective/removed (SIR) models can be solved exactly
on a wide variety of networks. In addition to the standard but unrealistic case
of fixed infectiveness time and fixed and uncorrelated probability of
transmission between all pairs of individuals, we solve cases in which times
and probabilities are non-uniform and correlated. We also consider one simple
case of an epidemic in a structured population, that of a sexually transmitted
disease in a population divided into men and women. We confirm the correctness
of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure
Correlations in Scale-Free Networks: Tomography and Percolation
We discuss three related models of scale-free networks with the same degree
distribution but different correlation properties. Starting from the
Barabasi-Albert construction based on growth and preferential attachment we
discuss two other networks emerging when randomizing it with respect to links
or nodes. We point out that the Barabasi-Albert model displays dissortative
behavior with respect to the nodes' degrees, while the node-randomized network
shows assortative mixing. These kinds of correlations are visualized by
discussig the shell structure of the networks around their arbitrary node. In
spite of different correlation behavior, all three constructions exhibit
similar percolation properties.Comment: 6 pages, 2 figures; added reference
Mixing patterns in networks
We study assortative mixing in networks, the tendency for vertices in
networks to be connected to other vertices that are like (or unlike) them in
some way. We consider mixing according to discrete characteristics such as
language or race in social networks and scalar characteristics such as age. As
a special example of the latter we consider mixing according to vertex degree,
i.e., according to the number of connections vertices have to other vertices:
do gregarious people tend to associate with other gregarious people? We propose
a number of measures of assortative mixing appropriate to the various mixing
types, and apply them to a variety of real-world networks, showing that
assortative mixing is a pervasive phenomenon found in many networks. We also
propose several models of assortatively mixed networks, both analytic ones
based on generating function methods, and numerical ones based on Monte Carlo
graph generation techniques. We use these models to probe the properties of
networks as their level of assortativity is varied. In the particular case of
mixing by degree, we find strong variation with assortativity in the
connectivity of the network and in the resilience of the network to the removal
of vertices.Comment: 14 pages, 2 tables, 4 figures, some additions and corrections in this
versio
Processos de democracia direta: sim ou não? Os argumentos clássicos à luz da teoria e da prática
Regularmente surgem controvérsias sobre os processos de democracia direta, dos quais os mecanismos mais frequentes são a iniciativa popular, o plebiscito e o referendo. Por um lado, há autores que defendem a posição de que essas instituições tornam o jogo político mais lento, caro, confuso e ilegítimo; outros defendem a posição contrária e argumentam que processos de democracia direta são fundamentais para os cidadãos e a qualidade da democracia. O presente estudo analisa esse tema em torno de sete questões, baseadas em considerações teóricas e pesquisas empíricas: 1. A questão entre o minimalismo e o maximalismo democrático; 2. A concorrência entre maioria e minoria; 3. A concorrência entre as instituições representativas e os processos de democracia direta; 4. A questão da competência dos cidadãos; 5. A questão dos efeitos colaterais dos processos de democracia direta; 6. A questão do tamanho do eleitorado; 7. A questão dos custos dos processos de democracia direta. As sete questões são analisadas a partir de uma revisão bibliográfica que considera tanto fontes nacionais como internacionais. O estudo mostra que os processos de democracia direta podem ser um complemento para as instituições representativas em um sistema democrático. O bom desempenho dos plebiscitos, referendos e iniciativas populares depende tanto da regulamentação destes como também do desempenho das outras instituições políticas e da situação socioeconômica de um país. O estudo permite ampliar e aprofundar o debate sobre processos de democracia direta no Brasil