Betweenness Centrality is not a Network Resilience Metric

Due to the recent expansion of the Web 2.0 -based services, along with the widespread of smartphones, online social network services are being popularized among users. Online social network services are the online community services which enable users to communicate each other, share information and expand human relationships. In the social network services, each relation between users is represented by a graph consisting of nodes and links. As the users of online social network services are increasing rapidly, the SNS are actively utilized in enterprise marketing, analysis of social phenomenon and so on. Social Network Analysis (SNA) is the systematic way to analyze social relationships among the members of the social network using the network theory. In general social network theory consists of nodes and arcs, and it is often depicted in a social network diagram. In a social network diagram, nodes represent individual actors within the network and arcs represent relationships between the nodes. With SNA, we can measure relationships among the people such as degree of intimacy, intensity of connection and classification of the groups. Ever since Social Networking Services (SNS) have drawn increasing attention from millions of users, numerous researches have made to analyze their user relationships and messages. There are typical representative SNA methods: degree centrality, betweenness centrality and closeness centrality. In the degree of centrality analysis, the shortest path between nodes is not considered. However, it is used as a crucial factor in betweenness centrality, closeness centrality and other SNA methods. In previous researches in SNA, the computation time was not too expensive since the size of social network was small. Unfortunately, most SNA methods require significant time to process relevant data, and it makes difficult to apply the ever increasing SNS data in social network studies. For instance, if the number of nodes in online social network is n, the maximum number of link in social network is n(n-1)/2. It means that it is too expensive to analyze the social network, for example, if the number of nodes is 10,000 the number of links is 49,995,000. Therefore, we propose a heuristic-based method for finding the shortest path among users in the SNS user graph. Through the shortest path finding method, we will show how efficient our proposed approach may be by conducting betweenness centrality analysis and closeness centrality analysis, both of which are widely used in social network studies. Moreover, we devised an enhanced method with addition of best-first-search method and preprocessing step for the reduction of computation time and rapid search of the shortest paths in a huge size of online social network. Best-first-search method finds the shortest path heuristically, which generalizes human experiences. As large number of links is shared by only a few nodes in online social networks, most nods have relatively few connections. As a result, a node with multiple connections functions as a hub node. When searching for a particular node, looking for users with numerous links instead of searching all users indiscriminately has a better chance of finding the desired node more quickly. In this paper, we employ the degree of user node vn as heuristic evaluation function in a graph G = (N, E), where N is a set of vertices, and E is a set of links between two different nodes. As the heuristic evaluation function is used, the worst case could happen when the target node is situated in the bottom of skewed tree. In order to remove such a target node, the preprocessing step is conducted. Next, we find the shortest path between two nodes in social network efficiently and then analyze the social network. For the verification of the proposed method, we crawled 160,000 people from online and then constructed social network. Then we compared with previous methods, which are best-first-search and breath-first-search, in time for searching and analyzing. The suggested method takes 240 seconds to search nodes where breath-first-search based method takes 1,781 seconds (7.4 times faster). Moreover, for social network analysis, the suggested method is 6.8 times and 1.8 times faster than betweenness centrality analysis and closeness centrality analysis, respectively. The proposed method in this paper shows the possibility to analyze a large size of social network with the better performance in time. As a result, our method would improve the efficiency of social network analysis, making it particularly useful in studying social trends or phenomena.

The betweenness centrality of a graph vertex measures how often this vertex is visited on shortest paths between other vertices of the graph. In the analysis of many real-world graphs or networks, the betweenness centrality of a vertex is used as an indicator for its relative importance in the network. In particular, it is among the most popular tools in social network analysis. In recent years, a growing number of real-world networks have been modeled as temporal graphs instead of conventional (static) graphs. In a temporal graph, we have a fixed set of vertices and there is a finite discrete set of time steps, and every edge might be present only at some time steps. While shortest paths are straightforward to define in static graphs, temporal paths can be considered “optimal” with respect to many different criteria, including length, arrival time, and overall travel time (shortest, foremost, and fastest paths). This leads to different concepts of temporal betweenness centrality, posing new challenges on the algorithmic side. We provide a systematic study of temporal betweenness variants based on various concepts of optimal temporal paths.Computing the betweenness centrality for vertices in a graph is closely related to counting the number of optimal paths between vertex pairs. While in static graphs computing the number of shortest paths is easily doable in polynomial time, we show that counting foremost and fastest paths is computationally intractable (#P-hard), and hence, the computation of the corresponding temporal betweenness values is intractable as well. For shortest paths and two selected special cases of foremost paths, we devise polynomial-time algorithms for temporal betweenness computation. Moreover, we also explore the distinction between strict (ascending time labels) and non-strict (non-descending time labels) time labels in temporal paths. In our experiments with established real-world temporal networks, we demonstrate the practical effectiveness of our algorithms, compare the various betweenness concepts, and derive recommendations on their practical use.

오피니언 마이닝과 네트워크 분석을 활용한 상품 커뮤니티 분석: 영화 흥행성과 예측 사례

Outlier detection has been used to detect and, where appropriate, remove anomalous observations from data. It has important applications in the field of fraud detection, network robustness analysis, and intrusion detection. In this paper, we propose a Betweenness Centrality (BEC) as novel to determine the outlier in network analyses. The Betweenness Centrality of a vertex in a graph is a measure for the participation of the vertex in the shortest paths in the graph. The Betweenness centrality is widely used in network analyses. Especially in a social network, the recursive computation of the betweenness centralities of vertices is performed for the community detection and finding the influential user in the network. In this paper, we propose that this method is efficient in finding outlier in social network analyses. Furthermore we show the effectiveness of the new methods using the experiments data.

Measuring the importance of a node in a network is a major goal in the analysis of social networks, biological systems, transportation networks etc. Different centrality measures have been proposed to capture the notion of node importance. For example, the center of a graph is a node that minimizes the maximum distance to any other node (the latter distance is the radius of the graph). The median of a graph is a node that minimizes the sum of the distances to all other nodes. Informally, the betweenness centrality of a node w measures the fraction of shortest paths that have w as an intermediate node. Finally, the reach centrality of a node w is the smallest distance r such that any s-t shortest path passing through w has either s or t in the ball of radius r around w.The fastest known algorithms to compute the center and the median of a graph, and to compute the betweenness or reach centrality even of a single node take roughly cubic time in the number n of nodes in the input graph. It is open whether these problems admit truly subcubic algorithms, i.e. algorithms with running time O(n3-δ) for some constant δ > 01.We relate the complexity of the mentioned centrality problems to two classical problems for which no truly subcubic algorithm is known, namely All Pairs Shortest Paths (APSP) and Diameter. We show that Radius, Median and Betweenness Centrality are equivalent under subcubic reductions to APSP, i.e. that a truly subcubic algorithm for any of these problems implies a truly subcubic algorithm for all of them. We then show that Reach Centrality is equivalent to Diameter under subcubic reductions. The same holds for the problem of approximating Betweenness Centrality within any constant factor. Thus the latter two centrality problems could potentially be solved in truly subcubic time, even if APSP requires essentially cubic time.

Measuring the importance of a node in a network is a major goal in the analysis of social networks, biological systems, transportation networks etc. Different centrality measures have been proposed to capture the notion of node importance. For example, the center of a graph is a node that minimizes the maximum distance to any other node (the latter distance is the radius of the graph). The median of a graph is a node that minimizes the sum of the distances to all other nodes. Informally, the betweenness centrality of a node w measures the fraction of shortest paths that have w as an intermediate node. Finally, the reach centrality of a node w is the smallest distance r such that any s-t shortest path passing through w has either s or t in the ball of radius r around w. The fastest known algorithms to compute the center and the median of a graph, and to compute the betweenness or reach centrality even of a single node take roughly cubic time in the number n of nodes in the input graph. It is open whether these problems admit truly subcubic algorithms, i.e. algorithms with running time Õ(n3–δ) for some constant δ > 01. We relate the complexity of the mentioned centrality problems to two classical problems for which no truly subcubic algorithm is known, namely All Pairs Shortest Paths (APSP) and Diameter. We show that Radius, Median and Betweenness Centrality are equivalent under subcubic reductions to APSP, i.e. that a truly subcubic algorithm for any of these problems implies a truly subcubic algorithm for all of them. We then show that Reach Centrality is equivalent to Diameter under subcubic reductions. The same holds for the problem of approximating Betweenness Centrality within any constant factor. Thus the latter two centrality problems could potentially be solved in truly subcubic time, even if APSP requires essentially cubic time.

The stability of social prominence and influence in a dynamic sow herd: A social network analysis approach

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 the edges. We develop the first axiomatic characterizations of all three measures. Our analysis shows that Random Walk Betweenness, while conceptually different, shares several common properties with classic Betweenness and Stress Centralities.

Network resilience to a disruption is generally considered to be a function of the initial impact of the disruption (the network’s vulnerability) and the trajectory of recovery after the disruption (the network’s recoverability). In the context of network resilience, this work develops and compares several flow-based importance measures to prioritize network edges for the implementation of preparedness options. For a particular preparedness option and particular geographically located disruption, we compare the different importance measures in their resulting network vulnerability, as well as network resilience for a general recovery strategy. Results suggest that a weighted flow capacity rate, which accounts for both (i) the contribution of an edge to maximum network flow and (ii) the extent to which the edge is a bottleneck in the network, shows most promise across four instances of varying network sizes and densities.

In addition to science citation indicators of journals like impact and immediacy, social network analysis provides a set of centrality measures like degree, betweenness, and closeness centrality. These measures are first analyzed for the entire set of 7,379 journals included in the Journal Citation Reports of the Science Citation Index and the Social Sciences Citation Index 2004 (Thomson ISI, Philadelphia, PA), and then also in relation to local citation environments that can be considered as proxies of specialties and disciplines. Betweenness centrality is shown to be an indicator of the interdisciplinarity of journals, but only in local citation environments and after normalization; otherwise, the influence of degree centrality (size) overshadows the betweenness‐centrality measure. The indicator is applied to a variety of citation environments, including policy‐relevant ones like biotechnology and nanotechnology. The values of the indicator remain sensitive to the delineations of the set because of the indicator's local character. Maps showing interdisciplinarity of journals in terms of betweenness centrality can be drawn using information about journal citation environments, which is available online.

In plants and other multicellular organisms, cells work together in tissues and organs to achieve outcomes that they would not be able to accomplish on their own. For example, the cells that make up the stem of a plant hold the leaves, flowers and other organs in place, and provide a transport network that allows molecules to move around the plant. Mapping the locations of cells within tissues and analysing the connections between them will help researchers to understand how the organisation of tissues influences the tasks cells perform. There are several different layers of tissue within a plant’s stem. The surface of the stem has a protective layer of tissue called epidermis. The epidermis contains two different types of cells known as trichoblasts and atrichoblasts, but it was not clear why these cells are organised the way they are. Arabidopsis thaliana is a small plant that is often used in studies of how plants grow and develop. Jackson et al. combined microscopy with computational techniques to study the stems of young A. thaliana seedlings. The experiments reveal that the two types of epidermal cells appear to adopt distinct roles. The trichoblasts form hair-like structures and acquire nutrients from the external environment, while their neighbours the atrichoblasts provide shortcut routes for these nutrients to be unloaded and moved up the stem. This pattern was not present in several other plant species including foxglove or poppy, suggesting it may be an adaptation in A. thaliana plants that helps them grow in the particular environments this plant faces. The findings of Jackson et al. show that cells are carefully arranged in plant stems and suggest that there is an optimal way for a plant to make a stem depending on its environment. Further work is now needed to understand how different molecules use the shortcuts provided by the atrichoblasts during plant development, and whether alternative configurations are possible. In the future, such studies may help provide a framework to genetically engineer plants that are better adapted to grow in different environments.

Betweenness-Centrality measure is often used in social and computer communication networks to estimate the potential monitoring and control capabilities a vertex may have on data flowing in the network. In this article, we define the Routing Betweenness Centrality (RBC) measure that generalizes previously well known Betweenness measures such as the Shortest Path Betweenness, Flow Betweenness, and Traffic Load Centrality by considering network flows created by arbitrary loop-free routing strategies. We present algorithms for computing RBC of all the individual vertices in the network and algorithms for computing the RBC of a given group of vertices, where the RBC of a group of vertices represents their potential to collaboratively monitor and control data flows in the network. Two types of collaborations are considered: (i) conjunctive—the group is a sequences of vertices controlling traffic where all members of the sequence process the traffic in the order defined by the sequence and (ii) disjunctive—the group is a set of vertices controlling traffic where at least one member of the set processes the traffic. The algorithms presented in this paper also take into consideration different sampling rates of network monitors, accommodate arbitrary communication patterns between the vertices (traffic matrices), and can be applied to groups consisting of vertices and/or edges. For the cases of routing strategies that depend on both the source and the target of the message, we present algorithms with time complexity of O ( n 2 m ) where n is the number of vertices in the network and m is the number of edges in the routing tree (or the routing directed acyclic graph (DAG) for the cases of multi-path routing strategies). The time complexity can be reduced by an order of n if we assume that the routing decisions depend solely on the target of the messages. Finally, we show that a preprocessing of O ( n 2 m ) time, supports computations of RBC of sequences in O ( kn ) time and computations of RBC of sets in O ( n 3 n ) time, where k in the number of vertices in the sequence or the set.

BackgroundA metabolic network is the sum of all chemical transformations or reactions in the cell, with the metabolites being interconnected by enzyme-catalyzed reactions. Many enzymes exist in numerous species while others occur only in a few. We ask if there are relationships between the phylogenetic profile of an enzyme, or the number of different bacterial species that contain it, and its topological importance in the metabolic network. Our null hypothesis is that phylogenetic profile is independent of topological importance. To test our null hypothesis we constructed an enzyme network from the KEGG (Kyoto Encyclopedia of Genes and Genomes) database. We calculated three network indices of topological importance: the degree or the number of connections of a network node; closeness centrality, which measures how close a node is to others; and betweenness centrality measuring how frequently a node appears on all shortest paths between two other nodes.ResultsEnzyme phylogenetic profile correlates best with betweenness centrality and also quite closely with degree, but poorly with closeness centrality. Both betweenness and closeness centralities are non-local measures of topological importance and it is intriguing that they have contrasting power of predicting phylogenetic profile in bacterial species. We speculate that redundancy in an enzyme network may be reflected by betweenness centrality but not by closeness centrality. We also discuss factors influencing the correlation between phylogenetic profile and topological importance.ConclusionOur analysis falsifies the hypothesis that phylogenetic profile of enzymes is independent of enzyme network importance. Our results show that phylogenetic profile correlates better with degree and betweenness centrality, but less so with closeness centrality. Enzymes that occur in many bacterial species tend to be those that have high network importance. We speculate that this phenomenon originates in mechanisms driving network evolution. Closeness centrality reflects phylogenetic profile poorly. This is because metabolic networks often consist of distinct functional modules and some are not in the centre of the network. Enzymes in these peripheral parts of a network might be important for cell survival and should therefore occur in many bacterial species. They are, however, distant from other enzymes in the same network.

Recent national level guidelines and research efforts increasingly suggest the use of resilience and sustainability concepts for natural hazard mitigation and recovery planning at the regional and community levels. This paper aims to distinguish and compare the two abstract concepts in the context of road networks recovering from a hazard event since resilience and sustainability metrics are often interchangeably adopted and can lead to inaccurate equivalencies between the two concepts. A spectrum of resilience and sustainability metrics are defined herein and a research methodology is described to evaluate them probabilistically. A case study demonstration on the road network in the Memphis Metropolitan Statistical Area (MMSA) for a probabilistic suite of earthquake scenarios shows that the correlation between network resilience and sustainability is dependent on the hazard level as well as the graphical abstraction of the real road network. While some correlations are observed between temporal sustainability metrics, such as missed trips and traffic emissions, and resilience metrics, like total travel distance and time, the correlation weakens as the network resolution becomes more sparse. These results show that while for dense networks, time-evolving travel time and travel distance may be used as proxy measures for hazard sustainability evolution, for sparsely connected networks, hazard resilience and post-hazard sustainability remain relatively distinct.

Relatively few studies have investigated the safety awareness and behavior that are substantially influenced by the characteristics of safety communication. It is very important to comprehend what kind of attributes play a role in adequate safety information flow in a communication network. For these reasons, the current study aimed to explore the effectiveness of safety communication on safety awareness and behavior. The data were collected by performing interviews with employees of teams at a liquefied natural gas terminal located in Pyeongtaek, South Korea. A social network analysis (SNA) was applied to visualize the pattern of the safety communication network and calculate the typical SNA metrics such as density, tie strength, betweenness and degree centrality. In addition, the number of communication channels was also considered as a crucial differentiator between teams. Then, a correlation analysis was applied to investigate the impact of calculated SNA metrics on safety awareness and behavior. As a result, density, tie strength, degree centrality and the channel variety showed a direct influence on safety awareness and behavior. Conversely, betweenness centrality was not an active metric. This study demonstrated that raising the level of SNA metrics such as density, tie strength and degree centrality, and using various channels to communicate safety information within teams, could support better safety awareness and behavior.