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At least 1,513 records · Page 84Linked to original sources
PubMed2002

Statistical properties and attack tolerance of growing networks with algebraic preferential attachment.

We consider growing networks with algebraic preferential attachment and address two questions: (1) what is the effect of temporal fluctuations in the number of new links acquired by the network? and (2) what is the network tolerance against random failures and intentional attacks? We find that the fluctuations generally have little effect on the network properties, although they lead to a plateau behavior for small degrees in the connectivity distribution. Formulas are derived for the evolution and distribution of the network connectivity, which are tested by numerical simulations. Numerical study of the effect of failures and attacks suggests that networks constructed under algebraic preferential attachment are more robust than scale-free networks.

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PubMed2002

Smallest small-world network.

Efficiency in passage times is an important issue in designing networks, such as transportation or computer networks. The small-world networks have structures that yield high efficiency, while keeping the network highly clustered. We show that among all networks with the small-world structure, the most efficient ones have a "single center" node, from which all shortcuts are connected to uniformly distributed nodes over the network. The networks with several centers and a connected subnetwork of shortcuts are shown to be "almost" as efficient. Genetic-algorithm simulations further support our results.

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PubMed2003

Reply networks on a bulletin board system.

Using data from a bulletin board system (BBS), we constructed reply networks for various boards, which can be considered as social networks connecting people of the same interests. In these networks, identifications (IDs) are treated as nodes and reply articles set up links. We investigated some statistics on these reply networks, such as clustering coefficients, characteristic path lengths, degree distributions, etc., and showed small-world characteristics and scale-free degree distributions of these reply networks. Then we put forward a model of interest space, which is the basis of the reply networks. We indicated that the hierarchical and clustering structure of the interest space, together with overlapping interests of IDs not only result in small-world characteristics of reply networks on BBS, but also give rise to preferential attachment, which is a popular explanation for scale-free features.

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PubMed2003

Self-organized critical neural networks.

A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics, which is estimated from an observable at the single synapse level. This principle is studied in a two-dimensional neural network with randomly wired asymmetric weights. In this class of networks, network connectivity is closely related to a phase transition between ordered and disordered dynamics. A slow topology change is imposed on the network through a local rewiring rule motivated by activity-dependent synaptic development: Neighbor neurons whose activity is correlated, on average develop a new connection while uncorrelated neighbors tend to disconnect. As a result, robust self-organization of the network towards the order disorder transition occurs. Convergence is independent of initial conditions, robust against thermal noise, and does not require fine tuning of parameters.

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PubMed2003

Network bipartivity.

Systems with two types of agents with a preference for heterophilous interaction produce networks that are more or less close to bipartite. We propose two measures quantifying the notion of bipartivity. The two measures-one well known and natural, but computationally intractable, and the other computationally less complex, but also less intuitive-are examined on model networks that continuously interpolate between bipartite graphs and graphs with many odd circuits. We find that the bipartivity measures increase as we tune the control parameters of the test networks to intuitively increase the bipartivity, and thus conclude that the measures are quite relevant. We also measure and discuss the values of our bipartivity measures for empirical social networks (constructed from professional collaborations, Internet communities, and field surveys). Here we find, as expected, that networks arising from romantic online interaction have high, and professional collaboration networks have low, bipartivity values. In some other cases, probably due to low average degree of the network, the bipartivity measures cannot distinguish between romantic and friendship oriented interaction.

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PubMed2003

Stochastically evolving networks.

We discuss a class of models for the evolution of networks in which new nodes are recruited into the network at random times, and links between existing nodes that are not yet directly connected may also form at random times. The class contains both models that produce "small-world" networks and less tightly linked models. We produce both trees, appropriate in certain biological applications, and networks in which closed loops can appear, which model communication networks and networks of human sexual interactions. One of our models is closely related to random recursive trees, and some exact results known in that context can be exploited. The other models are more subtle and difficult to analyze. Our analysis includes a number of exact results for moments, correlations, and distributions of coordination number and network size. We report simulations and also discuss some mean-field approximations. If the system has evolved for a long time and the state of a random node (which thus has a random age) is observed, power-law distributions for properties of the system arise in some of these models.

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PubMed2004

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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PubMed2004

Preferential exchange: strengthening connections in complex networks.

Many social, technological, and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available concerning the structure of many networks, the strengths are more difficult to measure. Here we show that, for one particular social network, notably the e-mail network, a suitable measure of the strength of the connections can be available. We also propose a simple mechanism, based on positive feedback and reciprocity, that can explain the observed behavior and that hints toward specific dynamics of formation and reinforcement of network connections. Network data from contexts different from social sciences indicate that power-law, and generally broad, distributions of the connection strength are ubiquitous, and the proposed mechanism has a wide range of applicability.

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PubMed2005

Self-avoiding walks on scale-free networks.

Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAW's) are expected to be more suitable than unrestricted random walks to explore various kinds of real-life networks. Here we study long-range properties of random SAW's on scale-free networks, characterized by a degree distribution P(k) approximately k(-gamma). In the limit of large networks (system size N-->infinity), the average number sn of SAW's starting from a generic site increases as mu(n) , with mu = k2/k-1 . For finite N, sn is reduced due to the presence of loops in the network, which causes the emergence of attrition of the paths. For kinetic growth walks, the average maximum length L increases as a power of the system size: L approximately Nalpha, with an exponent alpha increasing as the parameter gamma is raised. We discuss the dependence of alpha on the minimum allowed degree in the network. A similar power-law dependence is found for the mean self-intersection length of nonreversal random walks. Simulation results support our approximate analytical calculations.

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PubMed2005

Parallel dynamics and computational complexity of network growth models.

The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a power alpha of the connectivity of the existing node. Algorithms for generating growing networks very quickly in parallel are described and studied. The sublinear and superlinear cases require distinct algorithms. As a result, there is a discontinuous transition in the parallel complexity of sampling these networks corresponding to the discontinuous structural transition at alpha=1 , where the networks become scale-free. For alpha>1 , networks can be generated in constant time while for 0</=alpha<1 , logarithmic parallel time is required. The results show that these networks have little depth and embody very little history dependence despite being defined by sequential growth rules.

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PubMed2005

Efficient generation of large random networks.

Random networks are frequently generated, for example, to investigate the effects of model parameters on network properties or to test the performance of algorithms. Recent interest in the statistics of large-scale networks sparked a growing demand for network generators that can generate large numbers of large networks quickly. We here present simple and efficient algorithms to randomly generate networks according to the most commonly used models. Their running time and space requirement is linear in the size of the network generated, and they are easily implemented.

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PubMed2005

Network growth by copying.

We introduce a growing network model in which a new node attaches to a randomly selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultrasmall network where the average node degree grows logarithmically with network size while the network diameter equals 2. We determine basic geometrical network properties, such as the size dependence of the number of links and the in- and out-degree distributions. We also compare our predictions with real networks where the node degree also grows slowly with time--the Internet and the citation network of all Physical Review papers.

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PubMed2005

Noise-enhanced categorization in a recurrently reconnected neural network.

We investigate the interplay of recurrence and noise in neural networks trained to categorize spatial patterns of neural activity. We develop the following procedure to demonstrate how, in the presence of noise, the introduction of recurrence permits to significantly extend and homogenize the operating range of a feed-forward neural network. We first train a two-level perceptron in the absence of noise. Following training, we identify the input and output units of the feed-forward network, and thus convert it into a two-layer recurrent network. We show that the performance of the reconnected network has features reminiscent of nondynamic stochastic resonance: the addition of noise enables the network to correctly categorize stimuli of subthreshold strength, with optimal noise magnitude significantly exceeding the stimulus strength. We characterize the dynamics leading to this effect and contrast it to the behavior of a more simple associative memory network in which noise-mediated categorization fails.

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PubMed2005

Static pairwise annihilation in complex networks.

We study static annihilation on complex networks, in which pairs of connected particles annihilate at a constant rate during time. Through a mean-field formalism, we compute the temporal evolution of the distribution of surviving sites with an arbitrary number of connections. This general formalism, which is exact for disordered networks, is applied to Kronecker, Erdös-Rényi (i.e., Poisson), and scale-free networks. We compare our theoretical results with extensive numerical simulations obtaining excellent agreement. Although the mean-field approach applies in an exact way neither to ordered lattices nor to small-world networks, it qualitatively describes the annihilation dynamics in such structures. Our results indicate that the higher the connectivity of a given network element, the faster it annihilates. This fact has dramatic consequences in scale-free networks, for which, once the "hubs" have been annihilated, the network disintegrates and only isolated sites are left.

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PubMed2005

Voter model dynamics in complex networks: Role of dimensionality, disorder, and degree distribution.

We analyze the ordering dynamics of the voter model in different classes of complex networks. We observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks. We also find that when there is no ordering in the system, the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity. The existence of hubs, i.e., highly connected nodes, in the network modifies the linear system size scaling law of the survival time. The size of an ordered domain is sensitive to the network disorder and the average degree, decreasing with both; however, it seems not to depend on network size and on the heterogeneity of the degree distribution.

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PubMed2005

Core-periphery organization of complex networks.

Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy. We measure this coefficient for a number of real-world and model networks and find that different classes of networks have their characteristic values. Among other things we conclude that geographically embedded transportation networks have a strong core-periphery structure. We proceed to study radial statistics of the core, i.e., properties of the neighborhoods of the core vertices for increasing n. We find that almost all networks have unexpectedly many edges within n neighborhoods at a certain distance from the core suggesting an effective radius for nontrivial network processes.

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PubMed2006

Fluctuation-dissipation relations in complex networks.

In this paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing the susceptibilities of different networks to changes in external fields. In the case of networks with a given degree sequence, we argue that the scale-free topologies of real-world networks may arise as a result of the self-organization of real systems into sparse structures with low susceptibility to random external disruptions. We also show that the ensembles of networks with a given degree sequence and networks characterized by two-point correlations are equivalent to random networks with hidden variables.

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PubMed2006

Graph theoretic properties of networks formed by the Delaunay tessellation of protein structures.

The Delaunay tessellation of several sets of real and simplified model protein structures has been used to explore graph theoretic properties of residue contact networks. The system of contacts defined by residues joined by edges in the Delaunay simplices can be thought of as a graph or network and analyzed using techniques from elementary graph theory and the theory of complex networks. Such analysis indicates that protein contact networks have small world character, but technically are not small world networks. This approach also indicates that networks formed by native structures and by most misfolded decoys can be differentiated by their respective graph properties. The characteristic features of residue contact networks can be used for the detection of structural elements in proteins, such as the ubiquitous closed loops consisting of 22-32 consecutive residues, where terminal residues are Delaunay neighbors.

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