Search and Congestion in Complex Networks

Arenas, Àlex; Cabrales, Antonio; Dı́az-Guilera, Albert; Guimerà, Roger; Vega‐Redondo, Fernando

doi:10.1007/978-3-540-44943-0_11

Cited by 28 publications

(26 citation statements)

References 40 publications

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“…Physically this means that there will be more than one edge on average between two vertices that share a common neighbor. 25 This means in fact that the generating function formalism breaks down for α < 7 3 , invalidating some of the preceding results for the power-law graph, since a fundamental assumption of the method is that there are no short loops in the network. Aiello et al [8] get around this problem by assuming that the degree distribution is cut off at kmax ∼ n 1/α (see Sec.…”

Section: Example: Power-law Degree Distributionmentioning

confidence: 98%

The Structure and Function of Complex Networks

Newman¹

2003

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Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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Section: Example: Power-law Degree Distributionmentioning

confidence: 98%

The Structure and Function of Complex Networks

Newman¹

2003

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“…When one takes into account the fact that the shortest paths might not be known and instead a search algorithm is used for navigation (see Section 4.1), the betweenness of a vertex or edge must be defined in terms of the probability of it being visited by the search algorithm. This generalization, which was introduced by Arenas et al [109], subsumes the betweenness centrality based on random walks as proposed by Newman [110].…”

Section: Centrality Measurementsmentioning

confidence: 99%

Characterization of complex networks: A survey of measurements

Costa

Rodrigues

Travieso

et al. 2007

Advances in Physics

2,054

1,433

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Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.

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“…The Arenas-type random walk betweenness of v, motivated by [42] and based on the idea of searching a target, is the expected number of visits to v on a random walk that starts and ends at some randomly chosen nodes a, b:…”

Section: Measures Based On Random Walksmentioning

confidence: 99%

Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes

et al. 2012

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Abstract. When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite region or set of objects of interest. The selection procedure, e. g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized parts of the domain of interest. This heterogeneity may induce substantial bias and artifacts in derived network statistics. To avoid this bias, we propose an axiomatic scheme based on the idea of node splitting invariance to derive consistently weighted variants of various commonly used statistical network measures. The practical relevance and applicability of our approach is demonstrated for a number of example networks from different fields of research, and is shown to be of fundamental importance in particular in the study of spatially embedded functional networks derived from time series as studied in, e. g., neuroscience and climatology.

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Search and Congestion in Complex Networks

Cited by 28 publications

References 40 publications

The Structure and Function of Complex Networks

The Structure and Function of Complex Networks

Characterization of complex networks: A survey of measurements

Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes

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