Economic small-world behavior in weighted networks

By Vito Latora, Massimo Marchiori. 2002

779 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/10512503084161d6c6e1fe8f325f73c6f9b0632d

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Citations in the corpus

Age- and gender-related differences in the cortical anatomical network (2009, background): “The local clustering C and characteristic path length L of unweighted networks conceptually correspond to the local and global efficiency of weighted networks, respectively (Latora and Marchiori, 2003).”
Cognitive fitness of cost-efficient brain functional networks (2009, background): “Such ‘‘economical smallworld’’ properties—combining high efficiency with low connection cost—have been described for other biological and infrastructural systems (8) and may represent the outcome of evolutionary selection for both low cost and high efficiency of connections between network nodes (9–”
Parcellation‐dependent small‐world brain functional networks: A resting‐state fMRI study (2009, background): “Further work could be conducted by using continuous weighted correlation values in the construction of brain networks (Achard et al., 2006; Jiang et al. 2004; Latora and Marchiori, 2003).”
Method to find community structures based on information centrality. (2004, methodology): “In fact, instead of the edge betweenness, we adopt a measure of centrality, the information centrality C I [9, 10], based on the concept of eﬃcient propagation of information over the network [11, 12].”
Schizophrenia, neuroimaging and connectomics (2012, background): “Two related measures are network global and local efficiency (Latora and Marchiori, 2001, 2003).”
GRETNA: a graph theoretical network analysis toolbox for imaging connectomics (2015, background): “…386 clustering coefficient and characteristic path length (Watts and Strogatz, 1998; Onnela et al., 2005), local efficiency and global efficiency (Latora and Marchiori, 2001, 2003), modularity (Newman, 2006), assortativity (Newman, 2002; Leung and Chau, 2007), synchronization (Barahona and…”
A measure of centrality based on the network efficiency (2004, methodology): “In order to measure how eﬃciently the points of the network G exchange information, we use the network eﬃciency E , a quantity introduced in (Latora and Marchiori, 2001, 2003).”
BotGrep: Finding P2P Bots with Structured Graph Analysis (2010, background): “The information centrality of an edge is de-ﬁned as the relative network efﬁciency [46] drop caused by the removal of that.”
Efficiency and Cost of Economical Brain Functional Networks (2007, background): “, the minimum value of the sum of weights over all possible paths between nodes i and j [13].”
Spatial Networks (2010, background): “Another measure of efficiency was also proposed in [208, 209] and is defined as”
Cortical High-Density Counterstream Architectures (2013, background): “A simple measure of bandwidth for information transfer in complex networks can be defined via the average conductance between all source-target pairs in the network (85), called global efficiency, or (Eg).”
Small-World Brain Networks (2006, background): “One simple cost function is the sum of edges between regions in the graph (Latora and Marchiori 2003); a costly network will have many edges.”
A Predictive Network Model of Cerebral Cortical Connectivity Based on a Distance Rule (2013, neutral): “The global network communication efficiency measure Eg introduced by (Latora and Marchiori, 2003) is defined as:”
The Structure and Function of Complex Networks (2003, background): “Latora and Marchiori [260, 261] have considered the harmonic mean distance between a vertex and all others, which they call the “efficiency” of the vertex.”
The structure and dynamics of multilayer networks (2014, neutral): “This alternative definition is not equivalent to the previous one, and it is commonly used in the social sciences [87].”
Brain Connectivity (2011, background): “The clustering coefficient and inverse of the characteristic path length conceptually correspond to the local and global efficiency of a network, respectively (Latora and Marchiori 2003).”