Entropic Origin of Disassortativity in Complex Networks

Johnson, Samuel; Torres, Joaquı́n J.; Marro, Joaquín; Muñoz, Miguel A.

doi:10.1103/physrevlett.104.108702

Cited by 131 publications

(155 citation statements)

References 23 publications

Supporting

Mentioning

147

Contrasting

Unclassified

Order By: Relevance

“…(38) and λ q,q ′ ,α is the Lagrangian multiplier enforcing the constraint given by Eq. (39). The probability of a link between node i and node j in layer α is given by…”

Section: Multiplex Ensemble With Given Expected Degree Sequence In Eamentioning

confidence: 99%

See 1 more Smart Citation

Statistical mechanics of multiplex networks: Entropy and overlap

2013

View full text Add to dashboard Cite

There is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously. This is the case for example in social networks where each individual node has different kind of social ties or transportation systems where each location is connected to another location by different types of transport. Many of these multiplex are characterized by a significant overlap of the links in different layers. In this paper we introduce a statistical mechanics framework to describe multiplex ensembles. A multiplex is a system formed by N nodes and M layers of interactions where each node belongs to the M layers at the same time. Each layer α is formed by a network G α . Here we introduce the concept of correlated multiplex ensembles in which the existence of a link in one layer is correlated with the existence of a link in another layer. This implies that a typical multiplex of the ensemble can have a significant overlap of the links in the different layers. Moreover we characterize microcanonical and canonical multiplex ensembles satisfying respectively hard and soft constraints and we discuss how to construct multiplex in these ensembles. Finally we provide the expression for the entropy of these ensembles that can be useful to address different inference problems involving multiplexes.

show abstract

“…(38) and λ q,q ′ ,α is the Lagrangian multiplier enforcing the constraint given by Eq. (39). The probability of a link between node i and node j in layer α is given by…”

Section: Multiplex Ensemble With Given Expected Degree Sequence In Eamentioning

confidence: 99%

“…For single networks an equilibrium statistical mechanics framework has been recently formulated [30][31][32][33][34][35][36][37][38][39][40][41][42] in order to characterize network ensembles. A network ensemble is defined as a set of networks that satisfy a given number of structural constraints, i.e.…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics of multiplex networks: Entropy and overlap

2013

View full text Add to dashboard Cite

show abstract

“…For example, with 0 < r < 1 and m = 0, the approximate entropy is maximal for the sequence (N − 1,N − 2,..., N/2 , N/2 ,...,2,1); if m = 1 and N = 9, the maximum is realized by the sequence (8,8,7,7,6,6,4,4,4). A graph is regular if all its vertices have the same degree.…”

Section: Approximate Entropies Of a Networkmentioning

confidence: 99%

“…As a matter of fact, to describe mathematically the amount of heterogeneity and complexity found in natural and technological networks is nowadays a major endeavor in the frameworks provided by network theory, general data analysis, and inference. Several recent * jawest@gmail.com † lucas.lacasa@upm.es ‡ simoseve@gmail.com § a.teschendorff@ucl.ac.uk works point toward an entropic origin for a variety of key properties of complex networks that we find around us, such as the biodiversity maintenance in ecological networks [4,5], or, more generally, the emergence of robust degree-degree correlations [6] and communities in social and biological networks [7]. Indeed, the amount of heterogeneity in a network is a basic ingredient for quantifying properties of diffusion processes, such as the spread of human epidemics and computer viruses [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…An alternative is to try show that with high probability, one can construct a network (perhaps via the arguments of [29]) exploiting the "slack" gifted by the considerable nonuniqueness of slides. We have computed the first few terms of the sequence s 2 ,s 3 ,...,s 6 . The respective values are 3/4,3/8,13/16,20/32,58/64.…”

Section: Approximate Entropies Of a Networkmentioning

confidence: 99%

See 1 more Smart Citation

Approximate entropy of network parameters

et al. 2012

View full text Add to dashboard Cite

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

show abstract

Entropy‐based system assessment metric for determining architecture's robustness to different stakeholder perspectives

Ahn

Choi

Suh

2018

Systems Engineering

View full text Add to dashboard Cite

In this study, a new system assessment metric is proposed to evaluate the robustness of system architectures to different stakeholder perspectives and decomposition preferences. Typically, the decomposition of a system architecture into a modular configuration is based on the function‐based perspective of the design teams, which can be different from the perspectives of other stakeholders such as the manufacturing teams and field service organization. In this paper, a system architecture is decomposed into different modular configurations on the basis of the preferred perspectives of various stakeholders. The generated configurations are then compared to function‐based modular configurations in terms of the diffusion of the original function‐based module components into modules generated from different perspectives. The degree of diffusion is measured using a newly proposed entropy based metric referred to as the module diffusion index. The proposed metric provides stakeholders with a quantifiable measure of the robustness of a particular system architecture with respect to the preferred decomposition strategy of different stakeholders. The proposed metric can be used to assess different system architectures in terms of their robustness to perspective‐based decompositions. A case study is conducted wherein different mechanical clock architectures are assessed in terms of the robustness to different perspective‐based decompositions to demonstrate the effectiveness of the proposed metric.

show abstract

Entropic Origin of Disassortativity in Complex Networks

Cited by 131 publications

References 23 publications

Statistical mechanics of multiplex networks: Entropy and overlap

Statistical mechanics of multiplex networks: Entropy and overlap

Approximate entropy of network parameters

Entropy‐based system assessment metric for determining architecture's robustness to different stakeholder perspectives

Contact Info

Product

Resources

About