Betweenness centrality updation and community detection in streaming graphs using incremental algorithm
26 Feb 2017-pp 159-164
TL;DR: This paper computed betweenness centrality by identifying communities lying within the network by efficiently updates the centrality of the nodes whenever any edge or vertex addition or deletion takes place within the dynamic network by modifying solely a subset of vertices.
Abstract: Centrality measures have perpetually been helpful to find the foremost central or most powerful node within the network. There are numerous strategies to compute centrality of a node however in social networks betweenness centrality is the most widely used approach to bifurcate communities within the network, to find out the susceptibility within the complex networks and to generate the scale free networks whose degree distribution follows the power law. In this paper, we've computed betweenness centrality by identifying communities lying within the network. Our algorithm efficiently updates the centrality of the nodes whenever any edge or vertex addition or deletion takes place within the dynamic network by modifying solely a subset of vertices. For the vertex addition, Incremental Algorithm has been used in which Streaming graphs has also been considered. Brandes approach is the most widely used approach for finding out the betweenness centrality however it's still expensive for growing networks since it takes O(mn+n2logn) amount of time and O(n+m) space however our approach efficiently updates the centrality of the nodes by taking O(|S|n+|S|nlogn) amount of time where |S| is the subset of the vertices,m is the number of edges, n is the number of vertices and |S|≤n holds true.
Citations
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TL;DR: A new centrality for user is defined, applying susceptible-infected recovered (SIR) model to identify influence of users, and results show that the combination of behavioral and social characteristics would be determined the most influential users that influence majority of nodes on social networks.
Abstract: Purpose
This paper aims to analyze the role of influential nodes on other users on Facebook social media sites by social and behavioral characteristics of users. Hence, a new centrality for user is defined, applying susceptible-infected recovered (SIR) model to identify influence of users. Results show that the combination of behavioral and social characteristics would be determined the most influential users that influence majority of nodes on social networks.
Design/methodology/approach
In this paper, the authors define a new centrality for users, considering node status and behaviors. Thus, this node has a high level of influence. Node social status includes node degree, clustering coefficient and average neighbors’ node, and social status of node refers to user activities on Facebook social media website such as sending posts and receiving likes from other users. According to social status and user activity, the new centrality is defined. Finally, through the SIR model, the authors explore infection power of nodes and their influences of other node in the network.
Findings
Results show that the proposed centrality is more effective than other centrality approaches, infecting more nodes in social network. Another significant point in this research is that users who have high social status and activities on Facebook are more influential than users who have only high social status on the Facebook social media.
Originality/value
The influence of user on others in social media includes two key factors. The first factor is user social status such as node degree and clustering coefficient in social media graph and the second factor is related to user social activities in social media sites. Most centralities focused on node social status without considering node behavior. This paper analyzes the role of influential nodes on other users on Facebook social media site by social and behavioral characteristics of users.
22 citations
Posted Content•
TL;DR: This paper proves that the objective function of IMCPP under IC model is neither submodular nor supermodular, and forms the problem as a combinatorial optimization problem which aims at partitioning a given social network into disjoint M communities.
Abstract: Community partition is an important problem in many areas such as biology network, social network. The objective of this problem is to analyse the relationships among data via the network topology. In this paper, we consider the community partition problem under IC model in social networks. We formulate the problem as a combinatorial optimization problem which aims at partitioning a given social network into disjoint M communities. The objective is to maximize the sum of influence propagation of a social network through maximizing it within each community. The existing work shows the influence maximization for community partition problem (IMCPP) to be NP hard. We first prove that the objective function of IMCPP under IC model is neither submodular nor supermodular. Then both supermodular upper bound and submodular lower bound are constructed and proved so that the sandwich framework can be applied. A continuous greedy algorithm and a discrete implementation are designed for upper bound and lower bound problems and the algorithm for both of the two problems gets a 1-1/e approximation ratio. We also devise a simply greedy to solve the original objective function and apply the sandwich approximation framework to it to guarantee a data dependent approximation factor. Finally, our algorithms are evaluated on two real data sets, which clearly verifies the effectiveness of our method in community partition problem, as well as the advantage of our method against the other methods.
12 citations
Cites methods from "Betweenness centrality updation and..."
...A. Bhandari et al.[12] present a algorithm to compute the betweenness centrality of a node by detecting the community in the network....
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...Bhandari et al.[12] present a algorithm to compute the betweenness centrality of a node by detecting the community in the network....
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TL;DR: In this article , the authors considered the community partition problem under the independent cascade (IC) model in social networks and formulated the problem as a combinatorial optimization problem that aims at partitioning a given social network into disjoint communities.
Abstract: Community partition is an important problem in many areas, such as biology networks and social networks. The objective of this problem is to analyze the relationships among data via the network topology. In this article, we consider the community partition problem under the independent cascade (IC) model in social networks. We formulate the problem as a combinatorial optimization problem that aims at partitioning a given social network into disjoint $m$ communities. The objective is to maximize the sum of influence propagation of a social network through maximizing it within each community. The existing work shows that the influence maximization for community partition problem (IMCPP) is NP-hard. We first prove that the objective function of IMCPP under the IC model is neither submodular nor supermodular. Then, both supermodular upper bound and submodular lower bound are constructed and proved so that the sandwich framework can be applied. A continuous greedy algorithm and a discrete implementation are devised for upper and lower bound problems. The algorithm for both of the two problems gets a $1-1/e$ approximation ratio. We also present a simple greedy algorithm to solve the original objective function and apply the sandwich approximation framework to it to guarantee a data-dependent approximation factor. Finally, our algorithms are evaluated on three real datasets, which clearly verifies the effectiveness of our method in the community partition problem, as well as the advantage of our method against the other methods.
10 citations
TL;DR: The proposed method can be more effective in differentiating clusters and revealing relationship patterns among individual nodes and clusters in the network and is applied to a data of the semiconductor wafer manufacturing industry as a case study.
Abstract: Nowadays, the network data that we need to deal with and make sense of are becoming increasingly large and complex. Small-world networks are a type of complex networks whose underling graphs have small diameter, shorter average path length between nodes, and a high degree of clustering structures and can be found in a wide range of scientific fields, including social networks, sociology, computer science, business intelligence, and biology. However, conventional visualization algorithms for small-work networks lead to a uniform clump of nodes or are restricted to a tree structure, making the network structure difficult to identify and analyze. This work provides a new visual analytical method to improve the situation. Different from previous methods based on spanning trees, this method first generates a weighted planar sub-network based on the measurement of network centrality metrics. A force-directed algorithm based on node-edge repulsion is then applied to visualize this sub-network into a proper layout for better understanding of the data. Finally, the remaining links are placed back to maintain the original network’s integrity. The experimental results show that compared to previous methods, the proposed method can be more effective in differentiating clusters and revealing relationship patterns among individual nodes and clusters in the network. Furthermore, the proposed method is applied to a data of the semiconductor wafer manufacturing industry as a case study. The work shows that this new approach allows users to gain useful insights into the data.
8 citations
Cites background from "Betweenness centrality updation and..."
...In graph theory and network analysis, centrality is an indicator for finding important nodes and links (Bhandari et al. 2017; Bonchi et al. 2016; Freeman 1979; Opsahl et al. 2010)....
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...2.2 Network centrality In graph theory and network analysis, centrality is an indicator for finding important nodes and links (Bhandari et al. 2017; Bonchi et al. 2016; Freeman 1979; Opsahl et al. 2010)....
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TL;DR: A local search based heuristic whose performance is driven by two search strategies; a constructive greedy procedure that is employed to create an initial solution and a local improvement method that makes use of two neighborhood operators designed for exploring the search space of this problem.
Abstract: Over the past few years, the task of conceiving effective interventions on complex networks has arisen as different optimization problems. An interesting intervention scheme that has many important real-world applications is to introduce (infiltrate) in a network a certain number of new nodes and connect them to certain existing nodes with the aim of making them as central as possible. The idea is that they should occupy strategic positions in the network to gather a lot of information or to decisively influence others. In this work, we present an optimization problem that concerns the selection of nodes in a network with which to link each of a particular number of infiltrated nodes in order to maximize the lower betweenness centrality value obtained by them. This metric evaluates the participation of the nodes in the communications through the shortest paths of the network and it has been widely used as centrality measure in analyzing social networks. To address the problem, we propose a local search based heuristic whose performance is driven by two search strategies; a constructive greedy procedure that is employed to create an initial solution and a local improvement method that makes use of two neighborhood operators designed for exploring the search space of this problem. It should be noted that the development of metaheuristics for tackling combinatorial problems involving betweenness centrality is very challenging, because this measure is notoriously expensive to compute. That is why we have made two design decisions: firstly, to conceive a very simple metaheuristic approach and secondly, to incorporate in this proposal recent betweenness centrality update techniques that substantially reduce the number of shortest paths which should be re-computed when a network is changed. The performance of our optimizer, with respect to other metaheuristic models from the literature that can be adapted to face this problem, such as a randomized greedy multi-start algorithm and a steady-state genetic algorithm, is empirically shown.
4 citations
References
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TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
39,297 citations
"Betweenness centrality updation and..." refers background in this paper
...The degree of a node signifies that each node or vertex behaves in a different way within the complex network [4, 5, 6] and therefore centrality measures become necessary in such networks to order the vertices (shown in Figure 1)....
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01 Mar 1977
TL;DR: A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced in this paper, which define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication.
Abstract: A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced. These measures define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication. They may be used to index centrality in any large or small network of symmetrical relations, whether connected or unconnected.
8,026 citations
TL;DR: New algorithms for betweenness are introduced in this paper and require O(n + m) space and run in O(nm) and O( nm + n2 log n) time on unweighted and weighted networks, respectively, where m is the number of links.
Abstract: Motivated by the fast‐growing need to compute centrality indices on large, yet very sparse, networks, new algorithms for betweenness are introduced in this paper. They require O(n + m) space and run in O(nm) and O(nm + n2 log n) time on unweighted and weighted networks, respectively, where m is the number of links. Experimental evidence is provided that this substantially increases the range of networks for which centrality analysis is feasible. The betweenness centrality index is essential in the analysis of social networks, but costly to compute. Currently, the fastest known algorithms require ?(n 3) time and ?(n 2) space, where n is the number of actors in the network.
4,190 citations
Additional excerpts
...However, after few years in 2001, Brandes[8] proposed a brand new algorithm that reduced the running time of Freeman's approach....
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...Brandes Algorithm for dense network [21] can take O(n3) since m = n(n-1)/2 in the dense graph....
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...[8] U. Brandes, ’A faster algorithm for betweenness centrality’, The Journal of Mathematical Sociology, Vol. 25, No. 2, pp. 163-177, 2001....
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...It has been observed that if the target set S is chosen to be equal to V then this algorithm is almost same as Brandes in terms of speed but if S is less than V; then it takes O(|S|n+|S|nlogn) which would be far better in terms of complexity than O(mn+n2logn)....
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...Brandes approach is the most widely used approach for finding out the betweenness centrality however it's still expensive for growing networks since it takes O(mn+n2logn) amount of time and O(n+m) space however our approach efficiently updates the centrality of the nodes by taking O(|S|n+|S|nlogn) amount of time where |S| is the subset of the vertices,m is the number of edges, n is the number of vertices and |S| ≤ n holds true....
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TL;DR: This work introduces a class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes, and uses this benchmark to test two popular methods of community detection, modularity optimization, and Potts model clustering.
Abstract: Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e., the question of how good an algorithm is, with respect to others, is still open. Standard tests include the analysis of simple artificial graphs with a built-in community structure, that the algorithm has to recover. However, the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks. Here we introduce a class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes. We use this benchmark to test two popular methods of community detection, modularity optimization, and Potts model clustering. The results show that the benchmark poses a much more severe test to algorithms than standard benchmarks, revealing limits that may not be apparent at a first analysis.
2,772 citations
"Betweenness centrality updation and..." refers background or methods in this paper
...In large networks, community structure is first identified by Lancichinetti, [3] he observed that the nodes in the networks are generally group themselves into communities or modules such that the nodes which belong to the same community are similar whereas the nodes which are in different communities show less resemblance with each other....
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...[2] A. Lancichinetti, S. Fortunato and J. Kertesz, ’Detecting the overlapping and hierarchical community structure in complex networks’, New Journal of Physics, Vol. 11, No. 3, 2009....
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..., they are not assigned to any community [2, 3, 4]....
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...Several researchers [1,2,3] have shown that the networks are attributed by the heterogeneous degree distribution of a node that states that the node with the highest degree is placed at the top or is ranked the highest among all the nodes and therefore the one with the least degree is placed at the lowest....
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...The configuration model is used to connect the nodes so to keep their degree sequence [3]....
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Book•
14 May 2002
TL;DR: An ink jet comprises an elastic tubular member characterized by piezoelectric properties that is terminated in an orifice adapted to pass droplets of ink when the chamber formed within the tubular members is reduced in size.
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2,625 citations