Betweenness Centrality Index Research Articles

Identifying vital nodes in complex networks by adjacency information entropy

Identifying the vital nodes in networks is of great significance for understanding the function of nodes and the nature of networks. Many centrality indices, such as betweenness centrality (BC), eccentricity centrality (EC), closeness centricity (CC), structural holes (SH), degree centrality (DC), PageRank (PR) and eigenvector centrality (VC), have been proposed to identify the influential nodes of networks. However, some of these indices have limited application scopes. EC and CC are generally only applicable to undirected networks, while PR and VC are generally used for directed networks. To design a more applicable centrality measure, two vital node identification algorithms based on node adjacency information entropy are proposed in this paper. To validate the effectiveness and applicability of the proposed algorithms, contrast experiments are conducted with the BC, EC, CC, SH, DC, PR and VC indices in different kinds of networks. The results show that the index in this paper has a high correlation with the local metric DC, and it also has a certain correlation with the PR and VC indices for directed networks. In addition, the experimental results indicate that our algorithms can effectively identify the vital nodes in different networks.

An MCDM-based social network analysis of water governance to determine actors’ power in water-food-energy nexus

A major water governance concern is how to coordinate the complex relationships of the water, food, and energy sectors and the resulting economic, social, and environmental consequences. Focusing on the challenges in one sector (e.g. water shortage in the water sector) and making decisions without considering other sectors will not solve these problems; rather, it will create a new problem (the decline of food production) in the food sectors. The nexus approach is a novel method to represent the interrelated challenges of the water, food, and energy sectors by considering the sectors’ policies to achieve sustainable development. The present study analyzes the social network of nexus actors in the Yazd-Ardakan aquifer, Yazd province, Iran. For this purpose, 54 partners in the nexus network were first identified in various public, private, semi-private and non-governmental organizations. Three types of interactions (knowledge and information exchange, budget transfer, and collaboration) were analyzed among the actors. The actor-network was, then, assessed at the levels of the entire network and individual actors. Then, a coherence analysis was performed by the density index at the entire network level, and the power analysis was carried out using in-degree, out-degree, betweenness, closeness, and eigenvector centrality indices at the individual actor level. Social network analysis criteria were, then, incorporated with the multi-criteria decision-making model ELECTRE I to select the key and powerful actors in the nexus network. Next, the powerful actors were identified and introduced with respect to 15 criteria employed in the social network analysis. According to the results, the power structure in the nexus network of the research area is not at equilibrium. Most of the power lies with the public sector. The water, food, and energy sectors act alone and they do not exploit their maximum organizational capacities to establish relationships with one another.

Identifying critical edges in complex networks

The critical edges in complex networks are extraordinary edges which play more significant role than other edges on the structure and function of networks. The research on identifying critical edges in complex networks has attracted much attention because of its theoretical significance as well as wide range of applications. Considering the topological structure of networks and the ability to disseminate information, an edge ranking algorithm BCCMOD based on cliques and paths in networks is proposed in this report. The effectiveness of the proposed method is evaluated by SIR model, susceptibility index S and the size of giant component σ and compared with well-known existing metrics such as Jaccard coefficient, Bridgeness index, Betweenness centrality and Reachability index in nine real networks. Experimental results show that the proposed method outperforms these well-known methods in identifying critical edges both in network connectivity and spreading dynamic.

Development of the functional social network index for adolescent and young adult cancer survivors.

To the authors' knowledge, social network status in adolescent and young adult (AYA) cancer survivors has not been adequately studied to date. The authors developed and validated a functional social network index (FSNI) for AYA survivors, and compared its performance with that of 2 traditional indices (density and betweenness centrality). A total of 102 AYA survivors and 102 noncancer controls who were matched for age, sex, and race were recruited from an Internet panel. Each participant reported relationships with up to 25 close friends and/or relatives. The authors developed a FSNI with reported marital status, contact frequency with friends/relatives, available resources for emotional and tangible support, and available resources for physical activity and weight management advice. Linear regression was used to analyze associations between the FSNI and cancer diagnoses, treatments, and coping skills. Based on the FSNI, survivors were found to have more available resources for emotional support (beta [b] = 3.02; P = .003), tangible support (b = 4.17; P<.001), physical activity advice (b = 3.94; P<.001), and weight management advice (b = 4.10; P<.001) compared with noncancer controls. Survivors of lymphoma had the largest FSNI, whereas survivors of central nervous system malignancies had the smallest (b = 2.77; P = .02). A higher FSNI was associated with better coping skills: less denial (b = 0.10; P = .01), using emotional support (b = 0.08; P = .04), using instrumental support (b = 0.12; P<.001), less behavioral disengagement (b = 0.08; P = .04), venting of emotions (b = 0.10; P = .004), positive reframing (b = 0.12; P = .003), planning for the future (b = 0.08; P = .03), and religious engagement (b = 0.16; P<.001). Density and betweenness centrality indices demonstrated neither significant differences in social networks between cancer survivors and controls (all P values >.05) nor significant associations with coping skills (all P values >.05). The FSNI appears to provide a better social network assessment for AYA cancer survivors than traditional indices. Cancer 2018;124:2220-7. © 2018 American Cancer Society.

Graphical Classification in Multi-Centrality-Index Diagrams for Complex Chemical Networks

Various sizes of chemical reaction network exist, from small graphs of linear networks with several inorganic species to huge complex networks composed of protein reactions or metabolic systems. Huge complex networks of organic substrates have been well studied using statistical properties such as degree distributions. However, when the size is relatively small, statistical data suffers from significant errors coming from irregular effects by species, and a macroscopic analysis is frequently unsuccessful. In this study, we demonstrate a graphical classification method for chemical networks that contain tens of species. Betweenness and closeness centrality indices of a graph can create a two-dimensional diagram with information of node distribution for a complex chemical network. This diagram successfully reveals systematic sharing of roles among species as a semi-statistical property in chemical reactions, and distinguishes it from the ones in random networks, which has no functional node distributions. This analytical approach is applicable for rapid and approximate understanding of complex chemical network systems such as plasma-enhanced reactions as well as visualization and classification of other graphs.

Topological Robustness and Vulnerability Assessment of Water Distribution Networks

The reliability of a water distribution network (WDN) is a function of several time-invariant and time-dependent factors affecting its components and connectivity, most important of which have been shown to be the network’s topology, its operating pressure, the type of key components (such as the diameter, length, material and age of water pipes) and the network’s historical performance (such as the number of previously observed failures in the network). In terms of network topology, this attribute even though generally thought as time-invariant it actually is time-dependent, as the paths in a water distribution network change over time based on the hydraulics in the network (water demand and water pressure/flow alter the way water flows in the piping network). The work described herein examines the time-dependent nature of a WDN topology and by means of a betweenness centrality index (BC) method demonstrates the effect of topology on the network’s vulnerability / reliability. The importance of the betweenness centrality index is demonstrated by use of a case-study water distribution network operated under both normal and abnormal conditions. The proposed method is also coupled with spatial mapping to indicate areas of concern in the network, and with a decision support system to assist in prioritizing actions to improve on the network’s robustness and resilience.

Delineation of ecological security pattern based on ecological network

Ecological network can be used to describe and assess the relationship between spatial organization of landscapes and species survival under the condition of the habitat fragmentation. Taking Qingdao City as the research area, woodland and wetland ecological networks in 2005 were simulated based on least cost path method, and the ecological networks were classified by their corridors' cumulative cost value. We made importance distinction of ecological network structure elements such as patches and corridors using betweenness centrality index and correlation length-percentage of importance of omitted patches index, and then created the structure system of ecological network. Considering the effects brought by the newly-added construction land from 2005 to 2013, we proposed the ecological security pattern for construction land change of Qingdao City. The results showed that based on ecological network framework, graph theory based methods could be used to quantify both attributes of specific ecological land (e.g., the area of an ecological network patch) and functional connection between ecological lands. Between 2005 and 2013, large area of wetlands had been destroyed by newly-added construction land, while the role of specific woodland and wetland played in the connection of the whole network had not been considered. The delineation of ecological security pattern based on ecological network could optimize regional ecological basis, provide accurate spatial explicit decision for ecological conservation and restoration, and meanwhile provide scientific and reasonable space guidance for urban spatial expansion.

Research Trend Analysis of Geospatial Information in South Korea Using Text-Mining Technology

The purpose of this study was to analyze geospatial information (GI) research trends using text-mining techniques. Data were collected from 869 papers found in the Korea Citation Index (KCI) database (DB). Keywords extracted from these papers were classified into 13 GI domains and 13 research domains. We conducted basic statistical analyses (e.g., frequency and time series analyses) and network analyses, using such measures as frequency, degree, closeness centrality, and betweenness centrality, on the resulting domains. We subdivided the most frequent GI domain for more detailed analysis. Such processes permit an analysis of the relationships between the Research Fields associated with each GI. Our time series analysis found that the Climate and Satellite Image domain frequencies continuously increased. Satellite Image, General-Purpose Map, and Natural Disaster Map in the GI domain and Climate and Natural Disaster in the Research Field domain appeared in the center of the GI-Research Field network. We subdivided the Satellite Image domain for detailed analysis. As a result, LANDSAT, KOMPSAT, and MODIS displayed high scores on the frequency, degree, closeness centrality, and betweenness centrality indices. These results will be useful in GI-based interdisciplinary research and the selection of new research themes.

The condition of interdisciplinary communication among various Educational and Research Departments of Isfahan University of Medical Sciences.

BACKGROUND:The study aimed to assess interdisciplinary communication among various Educational and Research Departments of Isfahan University of Medical Sciences (IUMS) in clinical medical sciences using social network analysis.MATERIALS AND METHODS:The study was carried out using scientometrics method and interdisciplinary communication network analysis. Interdisciplinary network of 1298 articles in medical sciences published in Journal of Isfahan Medical School was evaluated using macro- and micro-level criteria of network analysis. Ravar Matrix, UCINET, and VOSviewer software were used to analyze the interdisciplinary network of medical sciences articles.RESULTS:Findings showed that “Students Research Committee” and “School of Medicine,” the affiliations of the medical students in general practice with scores of 272 and 197, “Epidemiology and Biostatistics,” “Community Medicine,” and “Internal Medicine” with 170, 101, and 99, respectively, possessed the first ranking of productivity index in scientific communication. Furthermore, in betweenness centrality index, “Epidemiology and Biostatistics” (3427.807), “Students Research Committee” (2967.180), and “Community Medicine” (1770.300) have an appropriate position in the network. Based on the centrality index, “Epidemiology and Biostatistics” (22.412), “Students Research Committee” (22.185) as well as “Community Medicine” and “School of Medicine” (both 21.554) acquired the least amount of distance with other nodes in network.CONCLUSION:Given the increased specialization in medical fields in recent years, communication between researchers with various specializations and creation of interdisciplinary or multidisciplinary departments had turned into an undeniable necessity. Therefore, communication between educational or research departments can facilitate the flow of information between researchers; and consequently, the top ranking departments in this study had more participation in scientific production of IUMS and getting more scores in annual evaluation by scientometrics department. This network analysis showed that researchers in various medical fields closely collaborate with each other and are able to connect with <2 intermediates.

Modified Betweenness-Based Measure for Prediction of Traffic Flow on Urban Roads

The conventional network structure measure, betweenness centrality (BC), has been used to predict roadway traffic flow; however, without consideration of variable travel demand on the roadway network, the measure’s prediction capability is limited by its static nature. With the objective of explicitly addressing the effects of travel pattern [e.g., origin–destination (O-D) distribution] on the prediction of urban roadway traffic flow, this paper proposes a modified measure that integrates the BC index and the traditional travel demand metrics (i.e., the O-D demand and the ratios of total demand). In the case study, roadway networks of two cities—San Francisco, California, and Nanjing, China—were selected to demonstrate the effectiveness of the proposed method. Taxi GPS trace data in the two cities were retrieved and applied to calibrate and validate the proposed measure. Correlation analyses were conducted to compare the predictions of the conventional and modified betweenness measures against the observed taxi traffic flows. The results show that, compared with the traditional approach, the modified betweenness measure produces predictions that have better correlations with the observed taxi traffic flows in both case studies. More accurate predictions for the future year traffic flow can be expected with the application of the new modified measure.

매개 중심성을 이용한 해양 플라스틱 폐기물의 경로 예측 및 효율적인 수거지점 제안

Korea severely suffers from plastic-induced ocean pollution, but only few studies predicted the trajectory of marine plastic debris and provided their collection method. This study used Ocean Surface CURrent Simulator (OSCURS) of National Oceanic and Atmospheric Administration (NOAA) in order to predict the trajectories of marine plastic debris flowing into the East Sea and Yellow Sea for each season during 2004 to 2013. Results suggest that efficient collection hubs through the high betweenness centrality index. Most hubs were located in the seashores regardless of season, suggesting the seashore of Uljin for the East Sea and the seashore between Saemangeum and Shinan for the Yellow Sea as the most efficient hubs.

Evaluating complex network indices for vulnerability analysis of a territorial power grid

In order to meet power demands in a sustainable way, power grids are gradually being adjusted to fit into a smart grid paradigm. A common problem in this kind of transition is to identify locations where it is most beneficial to invest in distributed generation. In order to assist in such a decision, we work on a graph model of a regional power grid. We apply optimization strategies on power flows, and verify the current degree of self-sufficiency of the network, with special reference to the effect of natural variations in wind-based production. We propose a method to assess collateral damage to the network resulting from a localized failure, and proceed to perform complex network analysis on multiple instances of the network, looking for correlations between estimated damages and betweenness centrality indices, with the purpose of attempting to determine which model is best suited to predict features of our network.

Brain Graph Topology Changes Associated with Anti-Epileptic Drug Use.

Neuroimaging studies of functional connectivity using graph theory have furthered our understanding of the network structure in temporal lobe epilepsy (TLE). Brain network effects of anti-epileptic drugs could influence such studies, but have not been systematically studied. Resting-state functional MRI was analyzed in 25 patients with TLE using graph theory analysis. Patients were divided into two groups based on anti-epileptic medication use: those taking carbamazepine/oxcarbazepine (CBZ/OXC) (n=9) and those not taking CBZ/OXC (n=16) as a part of their medication regimen. The following graph topology metrics were analyzed: global efficiency, betweenness centrality (BC), clustering coefficient, and small-world index. Multiple linear regression was used to examine the association of CBZ/OXC with graph topology. The two groups did not differ from each other based on epilepsy characteristics. Use of CBZ/OXC was associated with a lower BC. Longer epilepsy duration was also associated with a lower BC. These findings can inform graph theory-based studies in patients with TLE. The changes observed are discussed in relation to the anti-epileptic mechanism of action and adverse effects of CBZ/OXC.

Perspectives in systems biology

Perspectives in systems biology

A Model of Assessment of Collateral Damage on Power Grids based on Complex Network Theory

As power grids are gradually adjusted to fit into a smart grid paradigm, a common problem is to identify locations where it is most beneficial to introduce distributed generation. In order to assist in such a decision, we work on a graph model of a regional power grid, and propose a method to assess collateral damage to the network resulting from a localized failure. We perform complex network analysis on multiple instances of the network, looking for correlations between estimated damages and betweenness centrality indices, attempting to determine which model is best suited to predict features of our network.

The organisational structure of protein networks: revisiting the centrality–lethality hypothesis

Protein networks, describing physical interactions as well as functional associations between proteins, have been unravelled for many organisms in the recent past. Databases such as the STRING provide excellent resources for the analysis of such networks. In this contribution, we revisit the organisation of protein networks, particularly the centrality-lethality hypothesis, which hypothesises that nodes with higher centrality in a network are more likely to produce lethal phenotypes on removal, compared to nodes with lower centrality. We consider the protein networks of a diverse set of 20 organisms, with essentiality information available in the Database of Essential Genes and assess the relationship between centrality measures and lethality. For each of these organisms, we obtained networks of high-confidence interactions from the STRING database, and computed network parameters such as degree, betweenness centrality, closeness centrality and pairwise disconnectivity indices. We observe that the networks considered here are predominantly disassortative. Further, we observe that essential nodes in a network have a significantly higher average degree and betweenness centrality, compared to the network average. Most previous studies have evaluated the centrality-lethality hypothesis for Saccharomyces cerevisiae and Escherichia coli; we here observe that the centrality-lethality hypothesis hold goods for a large number of organisms, with certain limitations. Betweenness centrality may also be a useful measure to identify essential nodes, but measures like closeness centrality and pairwise disconnectivity are not significantly higher for essential nodes.

青岛市湿地生态网络评价与构建

Urban socio-economic development and spatial urban expansion has led to the loss and fragmentation of habitat.Global climate change adds to the gravity of these effects.An ecological network describes a network of habitats and connecting corridors that is mapped using habitat suitability and land use/land cover data.Connectivity within a habitat network ensures a flow of material,energy and information among the various patches,and allows species′ movement from inappropriate to appropriate areas.This ensures the abundance of species reaches a dynamic equilibrium at the network level and also means that the disappearance of species from any particular patch does not change the function of the regional ecosystem network.Thus,management of ecological network is an effective measure to counter the loss of biodiversity caused by reductions in habitat quality and area,as well as habitat fragmentation,in the context of rapid urbanization and climate change.The least cost path method is a way to construct and analyze ecological networks based on landscape spatial structure and dynamic biological processes.Based on the understanding that the characteristic of the matrix is one of the important factors determining the movement of species between patches,the least cost path method gives different cost values to different landscape types,and generates a cost surface to substitute the Euclidean space.Therefore,the dispersal paths generated by the least cost method are similar to those of actual species movement.Qingdao city is located in the eastern coastal region of China where the economy is relatively well-developed.The region is also where marine and terrestrial ecosystems meet.In this paper,we propose a wetland ecological network in the Qingdao district based on remote sensing and geographic information systems technology.We evaluate the overall structure of the network and the importance of individual patches using the correlation length index and betweenness centrality index,and use the findings to identify optimal strategies and make recommendations.In this paper,we discuss the following five questions:(1) How to classify landscapes?(2) How to determine the cost value of each landscape type?(3) How to evaluate the importance of each core patch?(4) How to evaluate the importance of stepping stones?(5) What is optimal management strategy for the wetland systems in the study area? The result shows that the network connectivities are very different in terms of threshold levels of path cost.Core patches in Jiao Zhou bay wetlands and Da Gu river have a relatively high degree of importance.Stepping stone patches with a high degree of importance are found in two zones: one comprising Jiao Zhou bay,Jiao Lai river and Wei He river estuary,and the other comprising Jiao Zhou bay and Ding Zi bay.In this paper,we propose a wetland management plan based on an ecological network including one core area,two axes and a ring in Qingdao and its surrounding area,to provide a scientific and quantitative basis for the selection of urban development sites within Qingdao City that simultaneously achieves wetland ecosystem protection.These network construction and evaluation methods can be used for other ecological network analysis.

A faster algorithm for betweenness centrality*

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.