Two betweenness centrality measures based on Randomized Shortest Paths

Kivimäki, Ilkka; Lebichot, Bertrand; Saramäki, Jari; Saerens, Marco

doi:10.1038/srep19668

Cited by 65 publications

(79 citation statements)

References 53 publications

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“…Their inverse temperature parameter also tunes the preference for geodesics. In [45], RSP is used to interpolate between graph distance and resistance distance, while in [46] it is used to interpolate between random-walk betweenness and a measure similar to standard betweenness centrality. In [47], Bavaud and Guex accomplish a weighting equivalent to RSP through the minimization of a free-energy functional.…”

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confidence: 99%

Absorbing random walks interpolating between centrality measures on complex networks

Gurfinkel

Rikvold

2020

Phys. Rev. E

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Centrality, which quantifies the importance of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs of nodes. Here we develop a method, based on absorbing Markov chains, that enables us to continuously interpolate both of these centrality measures away from the geodesic limit and toward a limit where no restriction is placed on the length of the paths the walkers can explore. At this second limit, the interpolated betweenness and closeness centralities reduce, respectively, to the well-known current betweenness and resistance closeness (information)centralities. The method is tested numerically on four real networks, revealing complex changes in node centrality rankings with respect to the value of the interpolation parameter. Non-monotonic betweenness behaviors are found to characterize nodes that lie close to inter-community boundaries in the studied networks.ity's preference for geodesics. However, these do not precisely reduce to the betweenness. Kivimäki et al . [45,46] introduce the randomized-shortest-path (RSP) framework, which assigns Boltzmann weights to all paths in the network. Their inverse temperature parameter also tunes the preference for geodesics. In [45], RSP is used to interpolate between graph distance and resistance distance, while in [46] it is used to interpolate between random-walk betweenness and a measure similar to standard betweenness centrality. In [47], Bavaud and Guex accomplish a weighting equivalent to RSP through the minimization of a free-energy functional. Françoisse et al . also reach similar results with a different path-weighting scheme in [48]. Estrada, Higham, and Hatano [25] calculate a version of betweenness centrality by assigning lower weights to longer paths.The remainder of this paper is organized as follows. In Sec. II A, we introduce notations and conventions. In Sec. II B, we discuss well-known centrality measures. In Sec. II C, we develop two new parametrized centralities, based on a specific absorbing random walk, that interpolate between (a) closeness and resistance-closeness centralities and (b) betweenness and random-walk betweenness centralities. In Sec. III A, we report the behavior of these centralities on four example networks. In Sec. III B, we use the numerical examples to explain how the presence of similarly-long paths leads to specific centrality behaviors. In Sec. III C, we provide a model for the non-monotonicity encountered in some of the numerics. In

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confidence: 99%

Absorbing random walks interpolating between centrality measures on complex networks

Gurfinkel

Rikvold

2020

Phys. Rev. E

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“…Further, in another study, the authors designed a factorial weighting scheme that favors paths of shorter lengths, called communicability betweenness 29 . Kivimaki et al 30 defined the framework of randomized shortest paths (RSP), which interpolates between the classic concept of shortest-path-based betweenness centrality and the random walk betweenness centrality through a temperature parameter. The canonical form of these measures is an average across all the paths starting from any source node and leading to any destination node, resulting in an estimate of the node's centrality in the global network topology.…”

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confidence: 99%

Discovering the genes mediating the interactions between chronic respiratory diseases in the human interactome

et al. 2020

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The molecular and clinical features of a complex disease can be influenced by other diseases affecting the same individual. Understanding disease-disease interactions is therefore crucial for revealing shared molecular mechanisms among diseases and designing effective treatments. Here we introduce Flow Centrality (FC), a network-based approach to identify the genes mediating the interaction between two diseases in a protein-protein interaction network. We focus on asthma and COPD, two chronic respiratory diseases that have been long hypothesized to share common genetic determinants and mechanisms. We show that FC highlights potential mediator genes between the two diseases, and observe similar outcomes when applying FC to 66 additional pairs of related diseases. Further, we perform in vitro perturbation experiments on a widely replicated asthma gene, GSDMB, showing that FC identifies candidate mediators of the interactions between GSDMB and COPD-associated genes. Our results indicate that FC predicts promising gene candidates for further study of disease-disease interactions.

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“…On the other hand, BPC's and BPCf's correlation with the other measures are less dependent of θ. Notice that it is expected that those measures should be highly correlated with RWB and EC when θ is small and with SPB when θ is large, as the bag-of-paths betweenness does [24]. However, we observe that the criticality measures BPC and BPCf are still more correlated with RWB when θ = 10.…”

Section: Resultsmentioning

confidence: 62%

A bag-of-paths node criticality measure

Lebichot

Saerens

2018

Neurocomputing

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This work compares several node (and network) criticality measures quantifying to which extend each node is critical with respect to the communication flow between nodes of the network, and introduces a new measure based on the Bag-of-Paths (BoP) framework. Network disconnection simulation experiments show that the new BoP measure outperforms all the other measures on a sample of Erdős-Rényi and Albert-Barabási graphs. Furthermore, a faster (still O(n 3 )), approximate, BoP criticality relying on the Sherman-Morrison rank-one update of a matrix is introduced for tackling larger networks. This approximate measure shows similar performances as the original, exact, one.

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Two betweenness centrality measures based on Randomized Shortest Paths

Cited by 65 publications

References 53 publications

Absorbing random walks interpolating between centrality measures on complex networks

Absorbing random walks interpolating between centrality measures on complex networks

Discovering the genes mediating the interactions between chronic respiratory diseases in the human interactome

A bag-of-paths node criticality measure

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