Economic Small-World Behavior in Weighted Networks
Vito Latora,Massimo Marchiori +1 more
TLDR
This paper proposes a generalization of the theory of small worlds based on two leading concepts, efficiency and cost, and valid also for weighted networks, and provides an adequate tool to quantitatively analyze the behaviour of complex networks in the real world.Abstract:
The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation is valid only for topological networks. In this paper we propose a generalization of the theory of small worlds based on two leading concepts, efficiency and cost, and valid also for weighted networks. Efficiency measures how well information propagates over the network, and cost measures how expensive it is to build a network. The combination of these factors leads us to introduce the concept of economic small worlds, that formalizes the idea of networks that are “cheap” to build, and nevertheless efficient in propagating information, both at global and local scale. In this way we provide an adequate tool to quantitatively analyze the behaviour of complex networks in the real world. Various complex systems are studied, ranging from the realm of neural networks, to social sciences, to communication and transportation networks. In each case, economic small worlds are found. Moreover, using the economic small-world framework, the construction principles of these networks can be quantitatively analyzed and compared, giving good insights on how efficiency and economy principles combine up to shape all these systems.read more
Citations
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Journal ArticleDOI
The Structure and Function of Complex Networks
TL;DR: Developments in this field are reviewed, 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.
Journal ArticleDOI
Complex brain networks: graph theoretical analysis of structural and functional systems
Edward T. Bullmore,Olaf Sporns +1 more
TL;DR: This article reviews studies investigating complex brain networks in diverse experimental modalities and provides an accessible introduction to the basic principles of graph theory and highlights the technical challenges and key questions to be addressed by future developments in this rapidly moving field.
Journal ArticleDOI
Complex networks: Structure and dynamics
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
Journal ArticleDOI
The structure and dynamics of multilayer networks
Stefano Boccaletti,Ginestra Bianconi,Regino Criado,Regino Criado,C.I. del Genio,Jesús Gómez-Gardeñes,Miguel Romance,Miguel Romance,Irene Sendiña-Nadal,Irene Sendiña-Nadal,Zhen Wang,Massimiliano Zanin +11 more
TL;DR: This work offers a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.
Journal ArticleDOI
Error and attack tolerance of complex networks
TL;DR: This work represents communication/transportation systems as networks and studies their ability to resist failures simulated as the breakdown of a group of nodes of the network chosen at random (chosen accordingly to degree or load).
References
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TL;DR: The authors' goal is always to offer you an assortment of cost-free ebooks too as aid resolve your troubles.
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The art of computer systems performance analysis
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