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Borm, Peter; Brink, van den R Rene; Slikker, Marco

doi:10.1023/a:1016339832755

Cited by 24 publications

(9 citation statements)

References 12 publications

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“…We select each node i (1 ≤ i ≤ N) as the initial location of the random walker with probability 1/N. For directed networks that are not necessarily strongly connected, Agaev-Chebotarev [10,11] and Borm et al [12] defined a centrality measure, which we call the influence and denote by v i without ambiguity, as the long-term probability that the walker visits node i. For a strongly connected network, v i is equal to the stationary density of the random walk and coincides with v i defined by Eq.…”

Section: Case Of Multiple Zero Laplacian Eigenvaluesmentioning

confidence: 99%

“…In the present study, we focus on another important class of centrality for directed networks, i.e., those derived from the Laplacian of the network. This class of centrality has a long history [7][8][9][10][11][12] and is mathematically close to the PageRank (see Sec. V).…”

Section: Introductionmentioning

confidence: 99%

“…Although the Laplacian-based centrality in the original form is applicable when all the nodes are reached along directed paths from a certain specified node, such a network is not generic. The Laplacian-based centrality has been generalized to the case of general directed networks [10][11][12]. In the generalized version, nodes in an uppermost component have positive centrality values, whereas nodes in a downstream component have zero centrality values (see Secs.…”

Section: Introductionmentioning

confidence: 99%

“…Networks do not have to be strongly connected and can be composed of disconnected components. The extended centrality measure, called as the influence or extended influence without ambiguity, is a one-parameter family of the centrality measure with parameter q such that the previous definition [10][11][12] is recovered in the limit q → 0. The extended influence is a relative of the PageRank; the influence and the PageRank correspond to continuous-time and discrete-time simple random walks, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics-based centrality for directed networks

Masuda

Kori

2010

Phys. Rev. E

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Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this respect is the PageRank. In this work, we focus on another class of centrality derived from the Laplacian of the network. We extend the Laplacian-based centrality, which has mainly been applied to strongly connected networks, to the case of general directed networks such that we can quantitatively compare arbitrary nodes. Toward this end, we adopt the idea used in the PageRank to introduce global connectivity between all the pairs of nodes with a certain strength. Numerical simulations are carried out on some networks. We also offer interpretations of the Laplacian-based centrality for general directed networks in terms of various dynamical and structural properties of networks. Importantly, the Laplacian-based centrality defined as the stationary density of the continuous-time random walk with random jumps is shown to be equivalent to the absorption probability of the random walk with sinks at each node but without random jumps. Similarly, the proposed centrality represents the importance of nodes in dynamics on the original network supplied with sinks but not with random jumps.

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Section: Case Of Multiple Zero Laplacian Eigenvaluesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamics-based centrality for directed networks

Masuda

Kori

2010

Phys. Rev. E

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“…Rubinstein (1980) eredményének általánosítására van den Brink és Gilles (2003) tanulmánya tett kísér-letet. A megoldási javaslatok közül érdemes még megemlíteni az invariáns és fair bets módszerekkel szoros kapcsolatban álló eljárást (Borm et al, 2002;Slikker et al, 2012), és a pozíciós erőt (positional power) (Herings et al, 2005). Korábban már mindkettőt bemutattuk , utóbbit részben itt is tárgyaljuk.…”

Section: A Pontozási Eljárások Axiomatikus Szempontú áTtekintéseunclassified