Betweenness Centrality (BC) is an important measure used widely in complex network analysis, such as social network, web page search, etc. Computing the exact BC values is highly time consuming. Currently the fastest exact BC determining algorithm is given by Brandes, taking $O(nm)$ time for unweighted graphs and $O(nm+n^2\log n)$ time for weighted graphs, where $n$ is the number of vertices and $m$ is the number of edges in the graph. Due to the extreme difficulty of reducing the time complexity of exact BC determining problem, many researchers have considered the possibility of any satisfactory BC approximation algorithms, especially those based on samplings. Bader et al. give the currently best BC approximation algorithm, with a high probability to successfully estimate the BC of one vertex within a factor of $1/\varepsilon$ using $\varepsilon t$ samples, where $t$ is the ratio between $n^2$ and the BC value of the vertex. However, some of the algorithmic parameters in Bader's work are not yet tightly bounded, leaving some space to improve their algorithm. In this project, we revisit Bader's algorithm, give more tight bounds on the estimations, and improve the performance of the approximation algorithm, i.e., fewer samples and lower factors. On the other hand, Riondato proposes a non-adaptive BC approximation method with samplings on shortest paths. We investigate the possibility to give an adaptive algorithm with samplings on vertices. With rigorous reasoning, we show that this algorithm can also give bounded approximation factors and number of samplings. To evaluate our results, we also conduct extensive experiments using real-world datasets, and find that both our algorithms can achieve acceptable performance. We verify that our work can improve the current BC approximation algorithm with better parameters, i.e., higher successful probabilities, lower factors and fewer samples.
Betweenness centrality quantifies the importance of a vertex for the information flow in a network. We propose a flexible definition of betweenness for temporal multiplexes, where geodesics are determined accounting for the topological and temporal structure and the duration of paths. We propose an algorithm to compute the new metric via a mapping to a static graph. We show the importance of considering the temporal multiplex structure and an appropriate distance metric comparing the results with those obtained with static or single-layer metrics on a dataset of $\sim 20$k European flights.
We perform the first axiomatic analysis of medial centrality measures. These measures, also called betweenness-like centralities, assess the role of a node in connecting others in the network. We focus on a setting with one target node and several source nodes. We consider three classic medial centrality measures adapted to this setting: Betweenness Centrality, Stress Centrality and Random Walk Betweenness Centrality. While Betweenness and Stress Centralities assume that the information in the network follows shortest paths, Random Walk Betweenness Centrality assumes it moves randomly along th…
There are several applications that benefit from a definition of centrality which is applicable to sets of vertices, rather than individual vertices. However, existing definitions might not be able to help us in answering several network analysis questions. In this paper, we study generalizing aggregation of centralities of individual vertices, to the centrality of the set consisting of these vertices. In particular, we propose exclusive betweenness centrality, defined as the number of shortest paths passing over exactly one of the vertices in the set, and discuss how this can be useful in det…
Betweenness centrality is a graph parameter that has been successfully applied to network analysis. In the context of computer networks, it was considered for various objectives, ranging from routing to service placement. However, as observed by Maccari et al. [INFOCOM 2018], research on betweenness centrality for improving protocols was hampered by the lack of a usable, fully distributed algorithm for computing this parameter. We resolve this issue by designing an efficient algorithm for computing betweenness centrality, which can be implemented by minimal modifications to any distance-vector…
Effective and efficient approximations of the generalized inverse of the graph Laplacian matrix with an application to current-flow betweenness centrality
In network analysis, the betweenness centrality of a node informally captures the fraction of shortest paths visiting that node. The computation of the betweenness centrality measure is a fundamental task in the analysis of modern networks, enabling the identification of the most central nodes in such networks. Additionally to being massive, modern networks also contain information about the time at which their events occur. Such networks are often called temporal networks. The temporal information makes the study of the betweenness centrality in temporal networks (i.e., temporal betweenness c…
Centrality measures are used in network science to evaluate the centrality of vertices or the position they occupy in a network. There are a large number of centrality measures according to some criterion. However, the generalizations of the most well-known centrality measures for weighted networks, degree centrality, closeness centrality, and betweenness centrality have solely assumed the edge weights to be constants. This paper proposes a methodology to generalize degree, closeness and betweenness centralities taking into account the variability of edge weights in the form of closed interval…
Betweenness centrality---measuring how many shortest paths pass through a vertex---is one of the most important network analysis concepts for assessing the relative importance of a vertex. The well-known algorithm of Brandes [J. Math. Sociol.~'01] computes, on an $n$-vertex and $m$-edge graph, the betweenness centrality of all vertices in $O(nm)$ worst-case time. In later work, significant empirical speedups were achieved by preprocessing degree-one vertices and by graph partitioning based on cut vertices. We contribute an algorithmic treatment of degree-two vertices, which turns out to be muc…
Recent research on finding important intermediate nodes in a network suspected to contain criminal activity is highly dependent on network centrality values. Betweenness centrality, for example, is widely used to rank the nodes that act as brokers in the shortest paths connecting all source and all the end nodes in a network. However both the shortest path node betweenness and the linearly scaled betweenness can only show rankings for all the nodes in a network. In this paper we explore the mathematical concept of pair-dependency on intermediate nodes, adapting the concept to criminal relation…
Betweenness centrality is a popular centrality measure with applications in several domains, and whose exact computation is impractical for modern-sized networks. We present SILVAN, a novel, efficient algorithm to compute, with high probability, accurate estimates of the betweenness centrality of all nodes of a graph and a high-quality approximation of the top-k betweenness centralities. SILVAN follows a progressive sampling approach, and builds on novel bounds based on Monte-Carlo Empirical Rademacher Averages, a powerful and flexible tool from statistical learning theory. SILVAN relies on a …
We describe a novel protocol for computing the egocentric betweenness centrality of a node when relevant edge information is spread between two mutually distrusting parties such as two telecommunications providers. While each node belongs to one network or the other, its ego network might include edges unknown to its network provider. We develop a protocol of differentially-private mechanisms to hide each network's internal edge structure from the other; and contribute a new two-stage stratified sampler for exponential improvement to time and space efficiency. Empirical results on several open…
A (Somewhat Dated) Comparative Study of Betweenness Centrality Algorithms on GPU
计算介数中心性（BC）的问题是很重要的分析图在许多实际应用中，如社交网络，生物网络，交通网络，电路等，因为这个问题是计算密集型，研究人员一直在开发算法，使用高性能的计算资源，如超级计算机，集群，图形处理单元（GPU）。当前用于计算BC的GPU算法采用Brandes的顺序算法，对于线程调度、数据结构和原子操作具有不同的折衷。在本文中，我们研究了三个GPU算法计算BC的未加权，有向，无标度网络。我们讨论和衡量他们的平衡线程调度，原子操作，同步和延迟隐藏的设计选择的权衡。我们的程序是用NVIDIA CUDA C编写的，并在NVIDIA Tesla M2050 GPU上测试。
Data classification is a major machine learning paradigm, which has been widely applied to solve a large number of real-world problems. Traditional data classification techniques consider only physical features (e.g., distance, similarity, or distribution) of the input data. For this reason, those are called \textit{low-level} classification. On the other hand, the human (animal) brain performs both low and high orders of learning and it has a facility in identifying patterns according to the semantic meaning of the input data. Data classification that considers not only physical attributes bu…
Betweenness centrality is one of the most popular vertex centrality measures in network analysis. Hence, many (sequential and parallel) algorithms to compute or approximate betweenness have been devised. Recent algorithmic advances have made it possible to approximate betweenness very efficiently on shared-memory architectures. Yet, the best shared-memory algorithms can still take hours of running time for large graphs, especially for graphs with a high diameter or when a small relative error is required. In this work, we present an MPI-based generalization of the state-of-the-art shared-memor…
About the Discriminant Power of the Subgraph Centrality and Other Centrality Measures About the Discriminant Power of the Subgraph Centrality and Other Centrality Measures(Working paper)
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 $\mathcal{NP}$-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, …
We propose the Temporal Walk Centrality, which quantifies the importance of a node by measuring its ability to obtain and distribute information in a temporal network. In contrast to the widely-used betweenness centrality, we assume that information does not necessarily spread on shortest paths but on temporal random walks that satisfy the time constraints of the network. We show that temporal walk centrality can identify nodes playing central roles in dissemination processes that might not be detected by related betweenness concepts and other common static and temporal centrality measures. We…
National University of Defense Technology（国防科技大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Tsinghua University（清华大学）；University of Pennsylvania（宾夕法尼亚大学）
Betweenness centrality (BC) is one of the most used centrality measures for network analysis, which seeks to describe the importance of nodes in a network in terms of the fraction of shortest paths that pass through them. It is key to many valuable applications, including community detection and network dismantling. Computing BC scores on large networks is computationally challenging due to high time complexity. Many approximation algorithms have been proposed to speed up the estimation of BC, which are mainly sampling-based. However, these methods are still prone to considerable execution tim…
Graph energy is the energy of the matrix representation of the graph, where the energy of a matrix is the sum of singular values of the matrix. Depending on the definition of a matrix, one can contemplate graph energy, Randić energy, Laplacian energy, distance energy, and many others. Although theoretical properties of various graph energies have been investigated in the past in the areas of mathematics, chemistry, physics, or graph theory, these explorations have been limited to relatively small graphs representing chemical compounds or theoretical graph classes with strictly defined properti…
Graph Centrality Measures for Boosting Popularity-Based Entity Linking
Labex Observatoire de la vie littéraire (OBVIL)（文学生活观察实验室）；Laboratoire d’Informatique de Paris 6 (LIP6), Pierre and Marie Curie University（巴黎第六大学计算机实验室）
Knowledge graphs play a central role for linking different data which leads to multiple layers. Thus, they are widely used in big data integration, especially for connecting data from different domains. Few studies have investigated the questions how multiple layers within graphs impact methods and algorithms developed for single-purpose networks, for example social networks. This manuscript investigates the impact of multiple layers on centrality measures compared to single-purpose graph. In particular, (a) we develop an experimental environment to (b) evaluate two different centrality measur…
