Characterization of complex networks: A survey of measurements

By Luciano da Fontoura Costa, Francisco Aparecido Rodrigues, Gonzalo Travieso, P. R. Villas Boas. 2005

2,367 citations recorded by the source corpus.

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.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/098f8f30867b1752d41a57877044c9813088c62d

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Citations in the corpus

Graph Theoretical Analysis of Functional Brain Networks: Test-Retest Evaluation on Short- and Long-Term Resting-State Functional MRI Data (2011, background): “However, there are still a lot of other network metrics, such as motif [72] and vulnerability [73] (for reviews, see [74,75]) whose TRT reliability need to be evaluated in future.”
Quantification of network structural dissimilarities (2017, background): “Important structural differences are missed or underestimated, because the measure employed considers graph properties that only partially describe the graphs 33 .”
Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography. (2009, background): “Vulnerability The vulnerability is widely used to quantitatively measure the damage on the network performance caused by the simulated failure of its elements (Costa et al. 2007).”
The Structure of Ecological Networks Across Levels of Organization (2020, background): “Multiple metrics are available to characterize interaction patterns at the node, link, and network levels (Costa et al. 2007).”
Knowledge transfer in a tourism destination: the effects of a network structure (2009, methodology): “Complex network analysis techniques were used to calculate the topological characteristics of the system (for definitions and formulas, see, e.g. da Fontoura Costa et al., 2007).”
Resisting structural re-identification in anonymized social networks (2008, background): “Figure 3 is an overview of the likelihood of re-identification under H1,H2,H3 and H4 knowledge queries.ForeachHi,thegraphreportsonthepercentageofnodes whosecandidatesetshavesizesinthefollowingbuckets:[1], [2,4], [5,10], [ 11 ,20], [21, ∞]. Nodes with candidate set size 1 have been uniquely identifie”
Water for food: The global virtual water trade network (2011, background): “…VOL. 47, W05520, doi:10.1029/2010WR010307, 2011 W05520 1 of 17 flexibility and generality for representing many natural structures [Barabási, 2002; Costa et al., 2007], including street systems [Kalapala et al., 2006;Masucci et al., 2009], the internet and World Wide Web [Barabási and Albert,…”