83,759 research outputs found
Dynamics of directed graphs: the world-wide Web
We introduce and simulate a growth model of the world-wide Web based on the
dynamics of outgoing links that is motivated by the conduct of the agents in
the real Web to update outgoing links (re)directing them towards constantly
changing selected nodes. Emergent statistical correlation between the
distributions of outgoing and incoming links is a key feature of the dynamics
of the Web. The growth phase is characterized by temporal fractal structures
which are manifested in the hierarchical organization of links. We obtain
quantitative agreement with the recent empirical data in the real Web for the
distributions of in- and out-links and for the size of connected component. In
a fully grown network of nodes we study the structure of connected clusters
of nodes that are accessible along outgoing links from a randomly selected
node. The distributions of size and depth of the connected clusters with a
giant component exhibit supercritical behavior. By decreasing the control
parameter---average fraction of updated and added links per time
step---towards the Web can resume a critical structure with
no giant component in it. We find a different universality class when the
updates of links are not allowed, i.e., for , corresponding to
the network of science citations.Comment: Revtex, 4 PostScript figures, small changes in the tex
Growing random networks with fitness
Three models of growing random networks with fitness dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes of connectivity and random additive fitness , with rate . For we find the connectivity distribution is power law with exponent . In the second model (B), the network is built by connecting nodes to nodes of connectivity , random additive fitness and random multiplicative fitness with rate . This model also has a power law connectivity distribution, but with an exponent which depends on the multiplicative fitness at each node. In the third model (C), a directed graph is considered and is built by the addition of nodes and the creation of links. A node with fitness , incoming links and outgoing links gains a new incoming link with rate , and a new outgoing link with rate . The distributions of the number of incoming and outgoing links both scale as power laws, with inverse logarithmic corrections
Resilience of Locally Routed Network Flows: More Capacity is Not Always Better
In this paper, we are concerned with the resilience of locally routed network
flows with finite link capacities. In this setting, an external inflow is
injected to the so-called origin nodes. The total inflow arriving at each node
is routed locally such that none of the outgoing links are overloaded unless
the node receives an inflow greater than its total outgoing capacity. A link
irreversibly fails if it is overloaded or if there is no operational link in
its immediate downstream to carry its flow. For such systems, resilience is
defined as the minimum amount of reduction in the link capacities that would
result in the failure of all the outgoing links of an origin node. We show that
such networks do not necessarily become more resilient as additional capacity
is built in the network. Moreover, when the external inflow does not exceed the
network capacity, selective reductions of capacity at certain links can
actually help averting the cascading failures, without requiring any change in
the local routing policies. This is an attractive feature as it is often easier
in practice to reduce the available capacity of some critical links than to add
physical capacity or to alter routing policies, e.g., when such policies are
determined by social behavior, as in the case of road traffic networks. The
results can thus be used for real-time monitoring of distance-to-failure in
such networks and devising a feasible course of actions to avert systemic
failures.Comment: Accepted to the IEEE Conference on Decision and Control (CDC), 201
Thesaurus as a complex network
A thesaurus is one, out of many, possible representations of term (or word)
connectivity. The terms of a thesaurus are seen as the nodes and their
relationship as the links of a directed graph. The directionality of the links
retains all the thesaurus information and allows the measurement of several
quantities. This has lead to a new term classification according to the
characteristics of the nodes, for example, nodes with no links in, no links
out, etc. Using an electronic available thesaurus we have obtained the incoming
and outgoing link distributions. While the incoming link distribution follows a
stretched exponential function, the lower bound for the outgoing link
distribution has the same envelope of the scientific paper citation
distribution proposed by Albuquerque and Tsallis. However, a better fit is
obtained by simpler function which is the solution of Ricatti's differential
equation. We conjecture that this differential equation is the continuous limit
of a stochastic growth model of the thesaurus network. We also propose a new
manner to arrange a thesaurus using the ``inversion method''.Comment: Contribution to the Proceedings of `Trends and Perspectives in
Extensive and Nonextensive Statistical Mechanics', in honour of Constantino
Tsallis' 60th birthday (submitted Physica A
Effects of Preference for Attachment to Low-degree Nodes on the Degree Distributions of a Growing Directed Network and a Simple Food-Web Model
We study the growth of a directed network, in which the growth is constrained
by the cost of adding links to the existing nodes. We propose a new
preferential-attachment scheme, in which a new node attaches to an existing
node i with probability proportional to 1/k_i, where k_i is the number of
outgoing links at i. We calculate the degree distribution for the outgoing
links in the asymptotic regime (t->infinity), both analytically and by Monte
Carlo simulations. The distribution decays like k c^k/Gamma(k) for large k,
where c is a constant. We investigate the effect of this
preferential-attachment scheme, by comparing the results to an equivalent
growth model with a degree-independent probability of attachment, which gives
an exponential outdegree distribution. Also, we relate this mechanism to simple
food-web models by implementing it in the cascade model. We show that the
low-degree preferential-attachment mechanism breaks the symmetry between in-
and outdegree distributions in the cascade model. It also causes a faster decay
in the tails of the outdegree distributions for both our network growth model
and the cascade model.Comment: 10 pages, 7 figures. A new figure added. Minor modifications made in
the tex
Accelerated growth in outgoing links in evolving networks: deterministic vs. stochastic picture
In several real-world networks like the Internet, WWW etc., the number of
links grow in time in a non-linear fashion. We consider growing networks in
which the number of outgoing links is a non-linear function of time but new
links between older nodes are forbidden. The attachments are made using a
preferential attachment scheme. In the deterministic picture, the number of
outgoing links at any time is taken as where is
the number of nodes present at that time. The continuum theory predicts a power
law decay of the degree distribution: , while the degree of the node introduced at time is given by
when the
network is evolved till time . Numerical results show a growth in the degree
distribution for small values at any non-zero . In the stochastic
picture, is a random variable. As long as is time-dependent, e.g.,
when follows a distribution . The behaviour
of changes significantly as is varied: for , the
network has a scale-free distribution belonging to the BA class as predicted by
the mean field theory, for smaller values of it shows different
behaviour. Characteristic features of the clustering coefficients in both
models have also been discussed.Comment: Revised text, references added, to be published in PR
Directed Accelerated Growth: Application in Citation Network
In many real world networks, the number of links increases nonlinearly with
the number of nodes. Models of such accelerated growth have been considered
earlier with deterministic and stochastic number of links. Here we consider
stochastic accelerated growth in a network where links are directed. With the
number of out-going links following a power law distribution, the results are
similar to the undirected case. As the accelerated growth is enhanced, the
degree distribution becomes independent of the ``initial attractiveness'', a
parameter which plays a key role in directed networks. As an example of a
directed model with accelerated growth, the citation network is considered, in
which the distribution of the number of outgoing link has an exponential tail.
The role of accelerated growth is examined here with two different growth laws.Comment: To be published in the proceedings of Statphys Kolkata V (Physica A
Topology of large-scale engineering problem-solving networks
The last few years have led to a series of discoveries that uncovered statistical properties that are common
to a variety of diverse real-world social, information, biological, and technological networks. The goal of the
present paper is to investigate the statistical properties of networks of people engaged in distributed problem
solving and discuss their significance. We show that problem-solving networks have properties ~sparseness,
small world, scaling regimes! that are like those displayed by information, biological, and technological
networks. More importantly, we demonstrate a previously unreported difference between the distribution of
incoming and outgoing links of directed networks. Specifically, the incoming link distributions have sharp
cutoffs that are substantially lower than those of the outgoing link distributions ~sometimes the outgoing
cutoffs are not even present!. This asymmetry can be explained by considering the dynamical interactions that
take place in distributed problem solving and may be related to differences between each actor’s capacity to
process information provided by others and the actor’s capacity to transmit information over the network. We
conjecture that the asymmetric link distribution is likely to hold for other human or nonhuman directed
networks when nodes represent information processing and using elements
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