A New Group Centrality Measure for Maximizing the Connectedness of Network Under Uncertain Connectivity

Fushimi, Takayasu; Saito, Kazumi; Ikeda, Tetsuo; Kazama, Kazuhiro

doi:10.1007/978-3-030-05411-3_1

Cited by 10 publications

(8 citation statements)

References 12 publications

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“…Puzis et al [43] state an algorithm for group betweenness maximization that does not utilize submodular approxima- tion but relies on a branch-and-bound approach. Alternative group centrality measures were introduced by Ishakian et al [25], Puzis et al [42], and Fushimi et al [21]. Ishakian et al defined single-vertex centrality measures based on a generic concept of path, and generalized them to groups of vertices.…”

Section: Related Workmentioning

confidence: 99%

Group Centrality Maximization for Large-scale Graphs

Angriman¹,

Grinten²,

Bojchevski³

et al. 2020

2020 Proceedings of the Twenty-Second Workshop on Algorithm Engineering and Experiments (ALENEX)

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The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central group is N P-hard. As a result, approximation algorithms to maximize group centralities were introduced recently. Despite a nearly-linear running time, approximation algorithms for group betweenness and (to a lesser extent) group closeness are rather slow on large networks due to high constant overheads.That is why we introduce GED-Walk centrality, a new submodular group centrality measure inspired by Katz centrality. In contrast to closeness and betweenness, it considers walks of any length rather than shortest paths, with shorter walks having a higher contribution. We define algorithms that (i) efficiently approximate the GED-Walk score of a given group and (ii) efficiently approximate the (proved to be N P-hard) problem of finding a group with highest GED-Walk score.Experiments on several real-world datasets show that scores obtained by GED-Walk improve performance on common graph mining tasks such as collective classification and graph-level classification. An evaluation of empirical running times demonstrates that maximizing GED-Walk (in approximation) is two orders of magnitude faster compared to group betweenness approximation and for group sizes ≤ 100 one to two orders faster than group closeness approximation. For graphs with tens of millions of edges, approximate GED-Walk maximization typically needs less than one minute. Furthermore, our experiments suggest that the maximization algorithms scale linearly with the size of the input graph and the size of the group.2 Katz centrality is sometimes alternatively defined based on walks ending at a given vertex; from an algorithmic perspective, however, this difference is irrelevant.

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Section: Related Workmentioning

confidence: 99%

Group Centrality Maximization for Large-scale Graphs

Angriman¹,

Grinten²,

Bojchevski³

et al. 2020

2020 Proceedings of the Twenty-Second Workshop on Algorithm Engineering and Experiments (ALENEX)

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“…Edge probabilities are mutually independent. This model is called a probabilistic network model and has been used widely to represent imperfect network data not only in social influence networks (Potamias et al 2010), but also in sensor networks (Gao et al 2017), opportunistic networks (Lu et al 2016), **protein-protein interaction networks (Srihari and Leong 2013) and road networks (Fushimi 2018). As each edge has two possible states (existing/non-existing) with probability p and 1 − p , each probabilistic graph corresponds to 2 |E| deterministic graphs which are called possible worlds (or instances), where each instance G i has an associated probability Pr(G i ) .…”

Section: Probabilistic Networkmentioning

confidence: 99%

Defining and measuring probabilistic ego networks

Kaveh

Magnani

Rohner

2020

Soc. Netw. Anal. Min.

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Analyzing ego networks to investigate local properties and behaviors of individuals is a fundamental task in social network research. In this paper we show that there is not a unique way of defining ego networks when the existence of edges is uncertain, since there are two different ways of defining the neighborhood of a node in such network models. Therefore, we introduce two definitions of probabilistic ego networks, called V-Alters-Ego and F-Alters-Ego, both rooted in the literature. Following that, we investigate three fundamental measures (degree, betweenness and closeness) for each definition. We also propose a method to approximate betweenness of an ego node among the neighbors which are connected via shortest paths with length 2. We show that this approximation method is faster to compute and it has high correlation with ego betweenness under the V-Alters-Ego definition in many datasets. Therefore, it can be a reasonable alternative to represent the extent to which a node plays the role of an intermediate node among its neighbors.

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“…In this paper, we substantially extended our previous study (Fushimi et al 2018) by adding new content as follows:…”

Section: Introductionmentioning

confidence: 99%

“…In this study, we aim to estimate the node connectedness and extract expected connected subgraphs under stochastic link disconnections. Assuming an uncertain graph, where link disconnection occurs stochastically-called edge-uncertainity-we have proposed a new centrality measure focusing on the degree of connectedness with neighboring nodes and an efficient sampling algorithm based on a time-evolving graph (Fushimi et al 2018). Although our method can be applied to general networks in principle, we target mainly spatial networks because urban road structures can be naturally regarded as uncertain graphs and few existing studies focus on such networks.…”

Section: Introductionmentioning

confidence: 99%

“…Although our method can be applied to general networks in principle, we target mainly spatial networks because urban road structures can be naturally regarded as uncertain graphs and few existing studies focus on such networks. In our previous study (Fushimi et al 2018), our method-connectedness centrality-defines the connectedness of each node as the expectation of the number of reachable nodes and attempts to extract nodes with high connectedness even when the graph is separated into several connected components by a link disconnection. In order to extract multiple nodes with high connectedness, we enhanced this method to group connectedness centrality, which selects nodes so as to maximize our objective function in a greedy manner.…”

Section: Introductionmentioning

confidence: 99%

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Estimating node connectedness in spatial network under stochastic link disconnection based on efficient sampling

et al. 2019

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Many networks including spatial networks, social networks, and web networks, are not deterministic but probabilistic due to the uncertainty of link existence. From networks with such uncertainty, to extract densely connected nodes, we propose connectedness centrality and its extended version, group connectedness centrality, where the connectedness of each node is defined as the expected size of its connected component over all possible graphs produced by an uncertain graph. In a large-scale network, however, since the number of combinations of possible graphs is enormous, it is difficult to strictly calculate the expected value. Therefore, we also propose an efficient estimation method based on Monte Carlo sampling. When applying our method to road networks, the extracted nodes can be regarded as candidate sites of evacuation facilities that many residents can reach even in the situation where roads are stochastically blocked by natural disasters. In our experimental evaluations using actual road networks, we show the following promising characteristics: our proposed method 1) works stably with respect to the number of simulations; 2) extracts nodes set reachable from more nodes even in a situation that many links are deleted; and 3) computes much more efficient, compared to existing centrality measures and community extraction methods.

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A New Group Centrality Measure for Maximizing the Connectedness of Network Under Uncertain Connectivity

Cited by 10 publications

References 12 publications

Group Centrality Maximization for Large-scale Graphs

Group Centrality Maximization for Large-scale Graphs

Defining and measuring probabilistic ego networks

Estimating node connectedness in spatial network under stochastic link disconnection based on efficient sampling

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