Optimal scales in weighted networks

Information theory fixes weighted networks’ degeneracy issues with a generalisation of binary graphs and an optimal scale of link intensities.

Social Informatics 8238, 1 (2013)

D. Garlaschelli, S. Ahnert, T. Fink, G. Caldarelli

Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks
Optimal scales in weighted networks

The analysis of networks characterized by links with heterogeneous intensity or weight suffers from two long-standing problems of arbitrariness. On one hand, the definitions of topological properties introduced for binary graphs can be generalized in non-unique ways to weighted networks. On the other hand, even when a definition is given, there is no natural choice of the (optimal) scale of link intensities (e.g. the money unit in economic networks). Here we show that these two seemingly independent problems can be regarded as intimately related, and propose a common solution to both. Using a formalism that we recently proposed in order to map a weighted network to an ensemble of binary graphs, we introduce an information-theoretic approach leading to the least biased generalization of binary properties to weighted networks, and at the same time fixing the optimal scale of link intensities. We illustrate our method on various social and economic networks.

More in Structure of how things relate

  • Nature Reviews Physics

    Physics of networks

    Statistical physics harnesses links between maximum entropy and information theory to capture null model and real-world network features.

  • Journal of Statistical Physics

    From ecology to finance

    Bipartite networks model the structures of ecological and economic real-world systems, enabling hypothesis testing and crisis forecasting.

  • EPL

    Clustering inverted

    Edge multiplicity—the number of triangles attached to edges—is a powerful analytic tool to understand and generalize network properties.

  • Physical Review E

    Weighted network evolution

    A statistical procedure identifies dominant edges within weighted networks to determine whether a network has reached its steady state.