A generalized approach to complex networks
L. da F. Costa,L. E.C. da Rocha +1 more
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TLDR
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models.Abstract:
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models. First, the concepts of node degree and clustering coefficient are extended in order to characterize not only specific nodes, but any generic subnetwork. Second, the consideration of distance transform and rings are used to further extend those concepts in order to obtain a signature, instead of a single scalar measurement, ranging from the single node to whole graph scales. The enhanced discriminative potential of such extended measurements is illustrated with respect to the identification of correspondence between nodes in two complex networks, namely a protein-protein interaction network and a perturbed version of it.read more
Citations
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Characterization of complex networks: A survey of measurements
TL;DR: In this paper, the authors present a survey of topological features of complex networks, including trajectories in several measurement spaces, correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification.
Journal ArticleDOI
Characterization of complex networks: A survey of measurements
TL;DR: This article presents a survey of measurements capable of expressing the most relevant topological features of complex networks and includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements.
Journal ArticleDOI
Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications
Luciano da Fontoura Costa,Osvaldo N. Oliveira,Gonzalo Travieso,Francisco A. Rodrigues,Paulino Ribeiro Villas Boas,Lucas Antiqueira,Matheus P. Viana,Luis E. C. Rocha +7 more
TL;DR: A diversity of phenomena are surveyed, which may be classified into no less than 11 areas, providing a clear indication of the impact of the field of complex networks.
Journal ArticleDOI
Analyzing and modeling real-world phenomena with complex networks: a survey of applications
Luciano da Fontoura Costa,Osvaldo N. Oliveira,Gonzalo Travieso,Francisco A. Rodrigues,Paulino Ribeiro Villas Boas,Lucas Antiqueira,Matheus P. Viana,Luis E. C. Rocha +7 more
TL;DR: The success of new scientific areas can be assessed by their potential in contributing to new theoretical approaches and in applications to real-world problems as mentioned in this paper, and complex networks have fared extremely well in both these aspects, with their sound theoretical basis being developed over the years and with a variety of applications.
Journal ArticleDOI
Rich-club phenomenon across complex network hierarchies
TL;DR: The authors investigate the existence of the rich-club phenomenon across the hierarchies of several real-world networks and reveal that the presence or absence of this phenomenon in a network does not imply its presence or presence in the network’s successive hierarchies, and that this behavior is even nonmonotonic in some cases.
References
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