Abstract: Social network theory is becoming more and more significant in social science, and the centrality measure is underlying this burgeoning theory. In perspective of social network, individuals, organizations, companies etc. are like nodes in the network, and centrality is used to measure these nodes’ power, activity, communication convenience and so on. Meanwhile, degree centrality, betweenness centrality and closeness centrality are the popular detailed measurements. This paper presents these 3 centrality in-depth, from principle to algorithm, and prospect good in the future use. Keywordssocial network; centrality; degree centrality; betweenness centrality; closeness centrality

Abstract: Network analysis is quickly gaining popularity in psychopathology research as a method that aims to reveal causal relationships among individual symptoms. To date, 4 main types of psychopathology networks have been proposed: (a) association networks, (b) regularized concentration networks, (c) relative importance networks, and (d) directed acyclic graphs. The authors examined the replicability of these analyses based on symptoms of major depression and generalized anxiety between and within 2 highly similar epidemiological samples (i.e., the National Comorbidity Survey-Replication [n = 9282] and the National Survey of Mental Health and Wellbeing [n = 8841]). Although association networks were stable, the 3 other types of network analysis (i.e., the conditional independence networks) had poor replicability between and within methods and samples. The detailed aspects of the models-such as the estimation of specific edges and the centrality of individual nodes-were particularly unstable. For example, 44% of the symptoms were estimated as the "most influential" on at least 1 centrality index across the 6 conditional independence networks in the full samples, and only 13-21% of the edges were consistently estimated across these networks. One of the likely reasons for the instability of the networks is the predominance of measurement error in the assessment of individual symptoms. The authors discuss the implications of these findings for the growing field of psychopathology network research, and conclude that novel results originating from psychopathology networks should be held to higher standards of evidence before they are ready for dissemination or implementation in the field. (PsycINFO Database Record

Abstract: Background Network analyses on psychopathological data focus on the network structure and its derivatives such as node centrality. One conclusion one can draw from centrality measures is that the node with the highest centrality is likely to be the node that is determined most by its neighboring nodes. However, centrality is a relative measure: knowing that a node is highly central gives no information about the extent to which it is determined by its neighbors. Here we provide an absolute measure of determination (or controllability) of a node – its predictability. We introduce predictability, estimate the predictability of all nodes in 18 prior empirical network papers on psychopathology, and statistically relate it to centrality. Methods We carried out a literature review and collected 25 datasets from 18 published papers in the field (several mood and anxiety disorders, substance abuse, psychosis, autism, and transdiagnostic data). We fit state-of-the-art network models to all datasets, and computed the predictability of all nodes. Results Predictability was unrelated to sample size, moderately high in most symptom networks, and differed considerable both within and between datasets. Predictability was higher in community than clinical samples, highest for mood and anxiety disorders, and lowest for psychosis. Conclusions Predictability is an important additional characterization of symptom networks because it gives an absolute measure of the controllability of each node. It allows conclusions about how self-determined a symptom network is, and may help to inform intervention strategies. Limitations of predictability along with future directions are discussed.

Abstract: The question of aggregating pairwise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g., MSR’s TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In most settings, in addition to obtaining a ranking, finding ‘scores’ for each object (e.g., player’s rating) is of interest for understanding the intensity of the preferences. In this paper, we propose Rank Centrality, an iterative rank aggregation algorithm for discovering scores for objects (or items) from pairwise comparisons. The algorithm has a natural random walk interpretation over the graph of objects with an edge present between a pair of objects if they are compared; the score, which we call Rank Centrality, of an object turns out to be its stationary probability under this random walk. To study the efficacy of the algorithm, we consider the popular Bradley-Terry-Luce (BTL) model (equ...

Abstract: Information cascades are important dynamical processes in complex networks. An information cascade can describe the spreading dynamics of rumour, disease, memes, or marketing campaigns, which initially start from a node or a set of nodes in the network. If conditions are right, information cascades rapidly encompass large parts of the network, thus leading to epidemics or epidemic spreading. Certain network topologies are particularly conducive to epidemics, while others decelerate and even prohibit rapid information spreading. Here we review models that describe information cascades in complex networks, with an emphasis on the role and consequences of node centrality. In particular, we present simulation results on sample networks that reveal just how relevant the centrality of initiator nodes is on the latter development of an information cascade, and we define the spreading influence of a node as the fraction of nodes that is activated as a result of the initial activation of that node. A systemic review of existing results shows that some centrality measures, such as the degree and betweenness, are positively correlated with the spreading influence, while other centrality measures, such as eccentricity and the information index, have negative correlation. A positive correlation implies that choosing a node with the highest centrality value will activate the largest number of nodes, while a negative correlation implies that the node with the lowest centrality value will have the same effect.We discuss possible applications of these results, and we emphasize how information cascades can help us identify nodes with the highest spreading capability in complex networks.

Abstract: Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with $N$ nodes as a sequence of $T$ layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supracentrality matrix of size $NT\times NT$ whose dominant eigenvector gives the centrality of each node $i$ at each time $t$. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node $i$ and the time layer $t$. We also introduce the concepts of marginal and conditional...

Abstract: Unlike many species that enact social behaviour in loose aggregations (such as swarms or herds), humans form groups comprising many long-term, intense, non-reproductive bonds with non-kin1. The cognitive demands of navigating such groups are thought to have significantly influenced human brain evolution2. Yet little is known about how and to what extent the human brain encodes the structure of the social networks in which it is embedded. We characterized the social network of an academic cohort (N = 275); a subset (N = 21) completed a functional magnetic resonance imaging (fMRI) study involving viewing individuals who varied in terms of ‘degrees of separation’ from themselves (social distance), the extent to which they were well-connected to well-connected others (eigenvector centrality) and the extent to which they connected otherwise unconnected individuals (brokerage). Understanding these characteristics of social network position requires tracking direct relationships, bonds between third parties and the broader network topology. Pairing network data with multi-voxel pattern analysis, we show that information about social network position is accurately perceived and spontaneously activated when encountering familiar individuals. These findings elucidate how the human brain encodes the structure of its social world and underscore the importance of integrating an understanding of social networks into the study of social perception. Parkinson et al. combine social network analysis and multi-voxel pattern analysis of functional magnetic resonance imaging data to show that the brain spontaneously encodes social distance, the centrality of the individuals encountered, and the extent to which they serve to broker connections between members.

Abstract: Many accounts of political belief systems conceive of them as networks of interrelated opinions, in which some beliefs are central and others peripheral. This article formally shows how such structural features can be used to construct direct measures of belief centrality in a network of correlations. This method is applied to the 2000 ANES data, which have been used to argue that political beliefs are organized around parenting schemas. This structural approach instead yields results consistent with the central role of political identity, which individuals may use as the organizing heuristic to filter information from the political field. In light of recent accounts of belief system heterogeneity, a search for population heterogeneity in this organizing logic was undertaken first by comparing 44 demographic subpopulations and then using inductive techniques. Contra these recent accounts, the study finds that belief systems of different groups vary in the amount of organization but not in the logic that o...

Abstract: We show that although the prominent centrality measures in network analysis make use of different information about nodes' positions, they all process that information in an identical way: they all spring from a common family that are characterized by the same simple axioms. In particular, they are all based on a monotonic and additively separable treatment of a statistic that captures a node's position in the network.

Abstract: In this article, we provide a brief tutorial on the estimation, analysis, and simulation on attitude networks using the programming language R. We first discuss what a network is and subsequently show how one can estimate a regularized network on typical attitude data. For this, we use open-access data on the attitudes toward Barack Obama during the 2012 American presidential election. Second, we show how one can calculate standard network measures such as community structure, centrality, and connectivity on this estimated attitude network. Third, we show how one can simulate from an estimated attitude network to derive predictions from attitude networks. By this, we highlight that network theory provides a framework for both testing and developing formalized hypotheses on attitudes and related core social psychological constructs.

Abstract: Identifying changes in the spatial structure of cities is a prerequisite for the development and validation of adequate planning strategies. Nevertheless, current methods of measurement are becomin...

Abstract: From free and open source software, through Wikipedia to video journalism, peer production plays a more significant role in the information production environment than was theoretically admissible by any economic model of motivation and organization that prevailed at the turn of the millennium. Its sustained success for a quarter of a century forces us to reevaluate three core assumptions of the standard models of innovation and production. First, it places intrinsic and social motivations, rather than material incentives, at the core of innovation, and hence growth. Second, it challenges the centrality of property, as opposed to the interaction of property and commons, to growth. And third, it questions the continued centrality of firms to the innovation process.

Abstract: Individuals benefit from occupying central roles in social networks, but little is known about the psychological traits that predict centrality. Across four college freshman dorms (n = 193), we characterized individuals with a battery of personality questionnaires and also asked them to nominate dorm members with whom they had different types of relationships. This revealed several social networks within dorm communities with differing characteristics. In particular, additional data showed that networks varied in the degree to which nominations depend on (i) trust and (ii) shared fun and excitement. Networks more dependent upon trust were further defined by fewer connections than those more dependent on fun. Crucially, network and personality features interacted to predict individuals' centrality: people high in well-being (i.e., life satisfaction and positive emotion) were central to networks characterized by fun, whereas people high in empathy were central to networks characterized by trust. Together, these findings provide network-based corroboration of psychological evidence that well-being is socially attractive, whereas empathy supports close relationships. More broadly, these data highlight how an individual's personality relates to the roles that they play in sustaining their community.

Abstract: Understanding how youth football players base their game interactions may constitute a solid criterion for fine-tuning the training process and, ultimately, to achieve better individual and team performances during competition. The present study aims to explore how passing networks and positioning variables can be linked to the match outcome in youth elite association football. The participants included 44 male elite players from under-15 and under-17 age groups. A passing network approach within positioning-derived variables was computed to identify the contributions of individual players for the overall team behaviour outcome during a simulated match. Results suggested that lower team passing dependency for a given player (expressed by lower betweenness network centrality scores) and high intra-team well-connected passing relations (expressed by higher closeness network centrality scores) were related to better outcomes. The correlation between the dyads' positioning regularity and the passing density showed a most likely higher correlation in under-15 (moderate effect), indicating a possible more dependence of the ball position rather than in the under-17 teams (small/unclear effects). Overall, this study emphasizes the potential of coupling notational analyses with spatial-temporal relations to produce a more functional and holistic understanding of teams' sports performance. Also, the social network analysis allowed to reveal novel key determinants of collective performance.

Abstract: In the field of complex networks, how to identify influential nodes in the network is still an important research topic. In this paper, a method to identify the influence of the node based on Analytic Hierarchy Process (AHP) is proposed. AHP, as a multiple attribute decision making (MADM) technique has become an important branch of decision making since then. Every centrality measure has its own disadvantages and limitations, thus we consider several different centrality measures as the multi-attribute of complex network in AHP application. AHP is used to aggregate the multi-attribute to obtain the evaluation of the influence of each node. The experiments on four real networks and an informative network show the efficiency and practicability of the proposed method.

Abstract: Online social networks (OSNs) have become a vital part of everyday living. OSNs provide researchers and scientists with unique prospects to comprehend individuals on a scale and to analyze human behavioral patterns. Influential spreaders identification is an important subject in understanding the dynamics of information diffusion in OSNs. Targeting these influential spreaders is significant in planning the techniques for accelerating the propagation of information that is useful for various applications, such as viral marketing applications or blocking the diffusion of annoying information (spreading of viruses, rumors, online negative behaviors, and cyberbullying). Existing K-core decomposition methods consider links equally when calculating the influential spreaders for unweighted networks. Alternatively, the proposed link weights are based only on the degree of nodes. Thus, if a node is linked to high-degree nodes, then this node will receive high weight and is treated as an important node. Conversely, the degree of nodes in OSN context does not always provide accurate influence of users. In the present study, we improve the K-core method for OSNs by proposing a novel link-weighting method based on the interaction among users. The proposed method is based on the observation that the interaction of users is a significant factor in quantifying the spreading capability of user in OSNs. The tracking of diffusion links in the real spreading dynamics of information verifies the effectiveness of our proposed method for identifying influential spreaders in OSNs as compared with degree centrality, PageRank, and original K-core.

Abstract: Community structure is an important area of research. It has received a considerable attention from the scientific community. Despite its importance, one of the key problems in locating information about community detection is the diverse spread of related articles across various disciplines. To the best of our knowledge, there is no current comprehensive review of recent literature which uses a scientometric analysis using complex networks analysis covering all relevant articles from the Web of Science (WoS). Here we present a visual survey of key literature using CiteSpace. The idea is to identify emerging trends besides using network techniques to examine the evolution of the domain. Towards that end, we identify the most influential, central, as well as active nodes using scientometric analyses. We examine authors, key articles, cited references, core subject categories, key journals, institutions, as well as countries. The exploration of the scientometric literature of the domain reveals that Yong Wang is a pivot node with the highest centrality. Additionally, we have observed that Mark Newman is the most highly cited author in the network. We have also identified that the journal, "Reviews of Modern Physics" has the strongest citation burst. In terms of cited documents, an article by Andrea Lancichinetti has the highest centrality score. We have also discovered that the origin of the key publications in this domain is from the United States. Whereas Scotland has the strongest and longest citation burst. Additionally, we have found that the categories of "Computer Science" and "Engineering" lead other categories based on frequency and centrality respectively.

Abstract: Based on emerging evidence, mood disorders can be plausibly conceptualized as networks of causally interacting symptoms, rather than as latent variables of which symptoms are passive indicators. In an innovative approach in nursing research, we used network analysis to estimate the network structure of 20 perinatal depressive (PND) symptoms. Then, two proof-of-principle analyses are presented: Incorporating stress and reproductive biomarkers into the network, and comparing the network structure of PND symptoms between non-depressed and depressed women. We analyzed data from a cross-sectional sample of 515 Latina women at the second trimester of pregnancy and estimated networks using regularized partial correlation network models. The main analysis yielded five strong symptom-to-symptom associations (e.g., cry-sadness), and five symptoms of potential clinical importance (i.e., high centrality) in the network. In exploring the relationship of PND symptoms to stress and reproductive biomarkers (proof-of-principle analysis 1), a few weak relationships were found. In a comparison of non-depressed and depressed women's networks (proof-of-principle analysis 2), depressed participants had a more connected network of symptoms overall, but the networks did not differ in types of relationships (the network structures). We hope this first report of PND symptoms as a network of interacting symptoms will encourage future network studies in the realm of PND research, including investigations of symptom-to-biomarker mechanisms and interactions related to PND. Future directions and challenges are discussed. © 2017 Wiley Periodicals, Inc.

Abstract: OBJECTIVE: To investigate how changes in functional network hierarchy determine cognitive impairment in multiple sclerosis (MS). METHODS: A cohort consisting of 332 patients with MS (age 48.1 ± 11.0 years, symptom duration 14.6 ± 8.4 years) and 96 healthy controls (HCs; age 45.9 ± 10.4 years) underwent structural MRI, fMRI, and extensive neuropsychological testing. Patients were divided into 3 groups: cognitively impaired (CI; n = 87), mildly cognitively impaired (MCI; n = 65), and cognitively preserved (CP; n = 180). The functional importance of brain regions was quantified with degree centrality, the average strength of the functional connections of a brain region with the rest of the brain, and eigenvector centrality, which adds to this concept by adding additional weight to connections with brain hubs because these are known to be especially important. Centrality values were calculated for each gray matter voxel based on resting-state fMRI data, registered to standard space. Group differences were assessed with a cluster-wise permutation-based method corrected for age, sex, and education. RESULTS: CI patients demonstrated widespread centrality increases compared to both HCs and CP patients, mainly in regions making up the default-mode network. Centrality decreases were similar in all patient groups compared to HCs, mainly in occipital and sensorimotor areas. Results were robust across centrality measures. CONCLUSIONS: Patients with MS with cognitive impairment show hallmark alterations in functional network hierarchy with increased relative importance (centrality) of the default-mode network.

Abstract: This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, k-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high k-path centrality have high node betweenness centrality. The randomized algorithm runs in time $O(\kappa^{3}n^{2-2\alpha}\log n)$ and outputs, for each vertex v, an estimate of its k-path centrality up to additive error of $\pm n^{1/2+ \alpha}$ with probability $1-1/n^2$. Experimental evaluations on real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared with existing randomized algorithms.

Abstract: We argue that the series of traits characterizing Borderline Personality Disorder samples do not weigh equally. In this regard, we believe that network approaches employed recently in Personality and Psychopathology research to provide information about the differential relationships among symptoms would be useful to test our claim. To our knowledge, this approach has never been applied to personality disorders. We applied network analysis to the nine Borderline Personality Disorder traits to explore their relationships in two samples drawn from university students and clinical populations (N = 1317 and N = 96, respectively). We used the Fused Graphical Lasso, a technique that allows estimating networks from different populations separately while considering their similarities and differences. Moreover, we examined centrality indices to determine the relative importance of each symptom in each network. The general structure of the two networks was very similar in the two samples, although some differences were detected. Results indicate the centrality of mainly affective instability, identity, and effort to avoid abandonment aspects in Borderline Personality Disorder. Results are consistent with the new DSM Alternative Model for Personality Disorders. We discuss them in terms of implications for therapy.