Random Walks on Complex Networks

Noh, Jae Dong; Rieger, Heiko

doi:10.1103/physrevlett.92.118701

Cited by 1,068 publications

(1,082 citation statements)

References 28 publications

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“…In particular, we use a random walk process and study the time needed until node visitation probabilities converge to a stationary state 37,38 . This convergence behaviour of a random walk is a simple proxy that captures the influence of both the topology and dynamics of temporal networks on general diffusive processes 39 . For a given convergence threshold E, we compute a slow-down factor S(E) that captures the slow-down of diffusive behaviour between the weighted aggregated network and a temporal network model derived from the empirical contact sequence, respectively (details in Methods section).…”

Section: Resultsmentioning

confidence: 99%

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

et al. 2014

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Recent research has highlighted limitations of studying complex systems with time-varying topologies from the perspective of static, time-aggregated networks. Non-Markovian characteristics resulting from the ordering of interactions in temporal networks were identified as one important mechanism that alters causality and affects dynamical processes. So far, an analytical explanation for this phenomenon and for the significant variations observed across different systems is missing. Here we introduce a methodology that allows to analytically predict causality-driven changes of diffusion speed in non-Markovian temporal networks. Validating our predictions in six data sets we show that compared with the time-aggregated network, non-Markovian characteristics can lead to both a slow-down or speed-up of diffusion, which can even outweigh the decelerating effect of community structures in the static topology. Thus, non-Markovian properties of temporal networks constitute an important additional dimension of complexity in time-varying complex systems.

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Section: Resultsmentioning

confidence: 99%

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

et al. 2014

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“…For instance, it remains to be seen whether target accessibility is predictive of mean waiting time in phenotype networks that are not fully connected. Recent analyses of random walks on weighted complex networks [22] may provide a useful starting point for this analysis.…”

Section: Discussionmentioning

confidence: 99%

Robustness, Evolvability, and Accessibility in Linear Genetic Programming

Payne

Banzhaf

et al. 2011

Lecture Notes in Computer Science

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Abstract. Whether neutrality has positive or negative effects on evolutionary search is a contentious topic, with reported experimental results supporting both sides of the debate. Most existing studies use performance statistics, e.g., success rate or search efficiency, to investigate if neutrality, either embedded or artificially added, can benefit an evolutionary algorithm. Here, we argue that understanding the influence of neutrality on evolutionary optimization requires an understanding of the interplay between robustness and evolvability at the genotypic and phenotypic scales. As a concrete example, we consider a simple linear genetic programming system that is amenable to exhaustive enumeration, and allows for the full characterization of these properties. We adopt statistical measurements from RNA systems to quantify robustness and evolvability at both genotypic and phenotypic levels. Using an ensemble of random walks, we demonstrate that the benefit of neutrality crucially depends upon its phenotypic distribution.

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“…In particular, random-walk centrality indices have been discussed by Noh and Rieger (2004) and Newman (2005). In this paper, we study the (unweighted) mean flow betwenness, defined for edges and vertices respectively (with complexity O(n 5 )) as…”

Section: Edge and Vertex Centrality Betweennessmentioning

confidence: 99%

Interpolating between Random Walks and Shortest Paths: A Path Functional Approach

Bavaud

Guex

2012

Lecture Notes in Computer Science

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Abstract. General models of network navigation must contain a deterministic or drift component, encouraging the agent to follow routes of least cost, as well as a random or diffusive component, enabling free wandering. This paper proposes a thermodynamic formalism involving two path functionals, namely an energy functional governing the drift and an entropy functional governing the diffusion. A freely adjustable parameter, the temperature, arbitrates between the conflicting objectives of minimising travel costs and maximising spatial exploration. The theory is illustrated on various graphs and various temperatures. The resulting optimal paths, together with presumably new associated edges and nodes centrality indices, are analytically and numerically investigated.

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Random Walks on Complex Networks

Cited by 1,068 publications

References 28 publications

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

Robustness, Evolvability, and Accessibility in Linear Genetic Programming

Interpolating between Random Walks and Shortest Paths: A Path Functional Approach

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