Node Centrality Measures Research Articles

Network topology of the Argentine interbank money market

AbstractThis article provides the first empirical network analysis of the Argentine interbank money market. Its main topological features are examined applying graph theory, focusing on the unsecured overnight loans settled from 2003 to 2017. The network, where banks are the nodes and the operations between them represent the links, exhibits low density, a higher reciprocity than comparable random graphs, short average distances and its clustering coefficient remains above that of a random network of equal size. Furthermore, the network is prominently disassortative. Its structural metrics experienced significant volatility, in correlation with the economic activity fluctuations and regulatory shifts. Signs of nodes’ random-like behaviour are detected during contractions. The degree distributions fit better to a Lognormal distribution than to a Poisson or a Power Law. Additionally, different node centrality measures are computed. It is found that a higher centrality enables a node to settle more convenient bilateral interest rates compared to the average market rate, identifying a statistical and economically significant effect by means of a regression analysis. These results constitute a relevant input for systemic risk assessment and provide solid empirical foundations for future theoretical modelling and shock simulations, especially in the context of underdeveloped financial systems.

Stability of network centrality measures: a numerical study

Identifying key actors or nodes in a network is a relevant task regarding many applications. In general, the real-valued function that evaluates the nodes is called node centrality measure. Performing a relevance-based ranking on the list of nodes is also of high practical importance, since the most central nodes by a measure usually provide the highest contribution in explaining the behavior of the whole network. Stability of centrality measures against graph perturbation is an important concept, especially in the analysis of real world—often noise contaminated—datasets from different domains. In this paper, with the utilization of the formal definition of stability introduced by Segarra and Ribeiro (IEEE Trans Signal Process 64(3):543–555, 2015), we discuss three main perturbation categories and experimentally analyze the stability of several node centrality measures.

Defense against malware propagation in complex heterogeneous networks

Devising appropriate defense strategies against malware propagation in complex networks with minimal budget is a challenging problem in research community. This paper studies and compares various immunization strategies such as random immunization, targeted immunization, acquaintance immunization and high-risk immunization to prevent the outbreak of malware. Also, three measures of node centrality (degree, closeness and betweenness) are taken into targeted immunization to slow down the malware propagation process. The malware propagation is modelled based on the susceptible–exposed–infected–recovered–susceptible with quarantine state (SEIRS-Q) epidemic model. Using numerical simulations, the model is verified with considering defense mechanisms in a synthetic (SFN) and a real (Facebook) network topology. The simulation results can help to better understand the effects of defense strategies against the malware propagation. The results show that the use of immunization and software diversity together are more effective than using each of them singly, in terms of reducing the density of infected node and halting malware propagation.

Distributed Estimation and Control of Node Centrality in Undirected Asymmetric Networks

Measures of node centrality that describe the importance of a node within a network are crucial for understanding the behavior of social networks and graphs. In this paper, we address the problems of distributed estimation and control of node centrality in undirected graphs with asymmetric weight values. In particular, we focus our attention on $\alpha$-centrality, which can be seen as a generalization of eigenvector centrality. In this setting, we first consider a distributed protocol where agents compute their $\alpha$-centrality, focusing on the convergence properties of the method; then, we combine the estimation method with a consensus algorithm to achieve a consensus value weighted by the influence of each node in the network. Finally, we formulate an $\alpha$-centrality control problem which is naturally decoupled and, thus, suitable for a distributed setting and we apply this formulation to protect the most valuable nodes in a network against a targeted attack, by making every node in the network equally important in terms of {\alpha}-centrality. Simulations results are provided to corroborate the theoretical findings.

A simple approach for quantifying node centrality in signed and directed social networks

The position of a node in a social network, or node centrality, can be quantified in several ways. Traditionally, it can be defined by considering the local connectivity of a node (degree) and some non-local characteristics (distance). Here, we present an approach that can quantify the interaction structure of signed digraphs and we define a node centrality measure for these networks. The basic principle behind our approach is to determine the sign and strength of direct and indirect effects of one node on another along pathways. Such an approach allows us to elucidate how a node is structurally connected to other nodes in the social network, and partition its interaction structure into positive and negative components. Centrality here is quantified in two ways providing complementary information: total effect is the overall effect a node has on all nodes in the same social network; while net effect describes, whether predominately positive or negative, the manner in which a node can exert on the social network. We use Sampson’s like-dislike relation network to demonstrate our approach and compare our result to those derived from existing centrality indices. We further demonstrate our approach by using Hungarian school classroom social networks.

NetEPD: A network-based essential protein discovery platform

Proteins drive virtually all cellular-level processes. The proteins that are critical to cell proliferation and survival are defined as essential. These essential proteins are implicated in key metabolic and regulatory networks, and are important in the context of rational drug design efforts. The computational identification of the essential proteins benefits from the proliferation of publicly available protein interaction datasets. Scientists have developed several algorithms that use these interaction datasets to predict essential proteins. However, a comprehensive web platform that facilitates the analysis and prediction of essential proteins is missing. In this study, we design, implement, and release NetEPD: a network-based essential protein discovery platform. This resource integrates data on Protein-Protein Interaction (PPI) networks, gene expression, subcellular localization, and a native set of essential proteins. It also computes a variety of node centrality measures, evaluates the predictions of essential proteins, and visualizes PPI networks. This comprehensive platform functions by implementing four activities, which include the collection of datasets, computation of centrality measures, evaluation, and visualization. The results produced by NetEPD are visualized on its website, and sent to a user-provided email, and they are available to download in a parsable format. This platform is freely available at http://bioinformatics.csu.edu.cn/netepd.

Scalable Spectral Clustering for Overlapping Community Detection in Large-Scale Networks

While the majority of methods for community detection produce disjoint communities of nodes, most real-world networks naturally involve overlapping communities. In this paper, a scalable method for the detection of overlapping communities in large networks is proposed. The method is based on an extension of the notion of normalized cut to cope with overlapping communities. A spectral clustering algorithm is formulated to solve the related cut minimization problem. When available, the algorithm may take into account prior information about the likelihood for each node to belong to several communities. This information can either be extracted from the available metadata or from node centrality measures. We also introduce a hierarchical version of the algorithm to automatically detect the number of communities. In addition, a new benchmark model extending the stochastic blockmodel for graphs with overlapping communities is formulated. Our experiments show that the proposed spectral method outperforms the state-of-the-art algorithms in terms of computational complexity and accuracy on our benchmark graph model and on five real-world networks, including a lexical network and large-scale social networks. The scalability of the proposed algorithm is also demonstrated on large synthetic graphs with millions of nodes and edges.

Beyond non-backtracking: non-cycling network centrality measures.

Walks around a graph are studied in a wide range of fields, from graph theory and stochastic analysis to theoretical computer science and physics. In many cases it is of interest to focus on non-backtracking walks; those that do not immediately revisit their previous location. In the network science context, imposing a non-backtracking constraint on traditional walk-based node centrality measures is known to offer tangible benefits. Here, we use the Hashimoto matrix construction to characterize, generalize and study such non-backtracking centrality measures. We then devise a recursive extension that systematically removes triangles, squares and, generally, all cycles up to a given length. By characterizing the spectral radius of appropriate matrix power series, we explore how the universality results on the limiting behaviour of classical walk-based centrality measures extend to these non-cycling cases. We also demonstrate that the new recursive construction gives rise to practical centrality measures that can be applied to large-scale networks.

Mapping language networks and their association with verbal abilities in paediatric epilepsy using MEG and graph analysis

Recent theoretical models of language have emphasised the importance of integration within distributed networks during language processing. This is particularly relevant to young patients with epilepsy, as the topology of the functional network and its dynamics may be altered by the disease, resulting in reorganisation of functional language networks. Thus, understanding connectivity within the language network in patients with epilepsy could provide valuable insights into healthy and pathological brain function, particularly when combined with clinical correlates. The objective of this study was to investigate interactions within the language network in a paediatric population of epilepsy patients using measures of MEG phase synchronisation and graph-theoretical analysis, and to examine their association with language abilities. Task dependent increases in connectivity were observed in fronto-temporal networks during verb generation across a group of 22 paediatric patients (9 males and 13 females; mean age 14 years). Differences in network connectivity were observed between patients with typical and atypical language representation and between patients with good and poor language abilities. In addition, node centrality in left frontal and temporal regions was significantly associated with language abilities, where patients with good language abilities had significantly higher node centrality within inferior frontal and superior temporal regions of the left hemisphere, compared to patients with poor language abilities. Our study is one of the first to apply task-based measures of MEG network synchronisation in paediatric epilepsy, and we propose that these measures of functional connectivity and node centrality could be used as tools to identify critical regions of the language network prior to epilepsy surgery.

Dynamic Properties of Foreign Exchange Complex Network

The foreign exchange (FX) market, one of the important components of the financial market, is a typical complex system. In this paper, by resorting to the complex network method, we use the daily closing prices of 41 FX markets to build the dynamical networks and their minimum spanning tree (MST) maps by virtue of a moving window correlation coefficient. The properties of FX networks are characterized by the normalized tree length, node degree distributions, centrality measures and edge survival ratios. Empirical results show that: (i) the normalized tree length plays a role in identifying crises and is negatively correlated with the market return and volatility; (ii) 83% of FX networks follow power-law node degree distribution, which means that the FX market is a typical heterogeneous market, and a few hub nodes play key roles in the market; (iii) the highest centrality measures reveal that the USD, EUR and CNY are the three most powerful currencies in FX markets; and (iv) the edge survival ratio analysis implies that the FX structure is relatively stable.

Modeling Epidemics in Seed Systems and Landscapes To Guide Management Strategies: The Case of Sweet Potato in Northern Uganda.

Seed systems are critical for deployment of improved varieties but also can serve as major conduits for the spread of seedborne pathogens. As in many other epidemic systems, epidemic risk in seed systems often depends on the structure of networks of trade, social interactions, and landscape connectivity. In a case study, we evaluated the structure of an informal sweet potato seed system in the Gulu region of northern Uganda for its vulnerability to the spread of emerging epidemics and its utility for disseminating improved varieties. Seed transaction data were collected by surveying vine sellers weekly during the 2014 growing season. We combined data from these observed seed transactions with estimated dispersal risk based on village-to-village proximity to create a multilayer network or “supranetwork.” Both the inverse power law function and negative exponential function, common models for dispersal kernels, were evaluated in a sensitivity analysis/ uncertainty quantification across a range of parameters chosen to represent spread based on proximity in the landscape. In a set of simulation experiments, we modeled the introduction of a novel pathogen and evaluated the influence of spread parameters on the selection of villages for surveillance and management. We found that the starting position in the network was critical for epidemic progress and final epidemic outcomes, largely driven by node out-degree. The efficacy of node centrality measures was evaluated for utility in identifying villages in the network to manage and limit disease spread. Node degree often performed as well as other, more complicated centrality measures for the networks where village-to-village spread was modeled by the inverse power law, whereas betweenness centrality was often more effective for negative exponential dispersal. This analysis framework can be applied to provide recommendations for a wide variety of seed systems.

Node centrality measures are a poor substitute for causal inference

Network models have become a valuable tool in making sense of a diverse range of social, biological, and information systems. These models marry graph and probability theory to visualize, understand, and interpret variables and their relations as nodes and edges in a graph. Many applications of network models rely on undirected graphs in which the absence of an edge between two nodes encodes conditional independence between the corresponding variables. To gauge the importance of nodes in such a network, various node centrality measures have become widely used, especially in psychology and neuroscience. It is intuitive to interpret nodes with high centrality measures as being important in a causal sense. Using the causal framework based on directed acyclic graphs (DAGs), we show that the relation between causal influence and node centrality measures is not straightforward. In particular, the correlation between causal influence and several node centrality measures is weak, except for eigenvector centrality. Our results provide a cautionary tale: if the underlying real-world system can be modeled as a DAG, but researchers interpret nodes with high centrality as causally important, then this may result in sub-optimal interventions.

Some properties of transportation network cooperative games

AbstractA basic question in network analysis concerns the quantification of the importance of each node in terms of network connectivity. To this end, a possible approach consists in using cooperative game theory tools to define a measure of node centrality. In this paper, given a transportation network, a cooperative game model with transferable utility (TU game) is considered. The nodes of the network represent the players in such a game, and the Shapley values of the nodes are used to measure centrality. The model, called Transportation Network cooperative (TNc) game, integrates within the utility function of the TU game the network topology and the demand. Properties of TNc games and their associated utility functions are investigated. Numerical results are reported, to get insights into the obtained properties.

Yükseköğretim Programı Tercihlerinin İncelenmesinde Karmaşık Ağ Analizi Yaklaşımı

In this study, we analyzed undergraduate program preferences of students by using complex network analysis techniques. We collected program preferences data from the YokAtlas portal provided by the Council of Higher Education using a web crawler we developed. We constructed a kind of co-occurrence network we called co-preference network of 622 nodes and 6,136 edges from the collected raw data. We performed a comprehensive exploratory complex network analysis on the co-preference network using Cytoscape and NodeXL tools. Using several node centrality measures, we identified the most popular programs that students frequently preferred together with other programs. In addition, we observed the clusters of programs embedded in the network using several network community detection methods. Finally, we performed a structure analysis to compare our network to a corresponding random network, and we showed that our network had the common characteristic properties that many real-world networks exhibit.

Network model-based analysis of the goals, targets and indicators of sustainable development for strategic environmental assessment

Strategic environmental assessment is a decision support technique that evaluates policies, plans and programs in addition to identifying the most appropriate interventions in different scenarios. This work develops a network-based model to study interlinked ecological, economic, environmental and social problems to highlight the synergies between policies, plans, and programs in environmental strategic planning. Our primary goal is to propose a methodology for the data-driven verification and extension of expert knowledge concerning the interconnectedness of the sustainable development goals and their related targets. A multilayer network model based on the time-series indicators of the World Bank open data over the last 55 years was assembled. The results illustrate that by providing an objective and data-driven view of the correlated variables of the World Bank, the proposed layered multipartite network model highlights the previously not discussed interconnections, node centrality measures evaluate the importance of the targets, and network community detection algorithms reveal their strongly connected groups. The results confirm that the proposed methodology can serve as a data-driven decision support tool for the preparation and monitoring of long-term environmental policies. The developed new data-driven network model enables multi-level analysis of the sustainability (goals, targets, indicators) and will make it possible to plan long-term environmental strategic planning. Through relationships among indicators, relationships among targets and goals can be modelled. The results show that sustainable development goals are strongly interconnected, while the 5th goal (gender equality) is linked mostly to 17th (partnerships for the goals) goal. The analysis has also highlighted the importance of the 4th (quality education).

Enumerating Connected Subgraphs and Computing the Myerson and Shapley Values in Graph-Restricted Games

At the heart of multi-agent systems is the ability to cooperate to improve the performance of individual agents and/or the system as a whole. While a widespread assumption in the literature is that such cooperation is essentially unrestricted, in many realistic settings this assumption does not hold. A highly influential approach for modelling such scenarios are graph-restricted games introduced by Myerson [36]. In this approach, agents are represented by nodes in a graph, edges represent communication channels, and a group can generate an arbitrary value only if there exists a direct or indirect communication channel between every pair of agents within the group. Two fundamental solution-concepts that were proposed for such games are the Myerson value and the Shapley value . While an algorithm has been developed to compute the Shapley value in arbitrary graph-restricted games, no such general-purpose algorithm has been developed for the Myerson value to date. With this in mind, we set out to develop for such games a general-purpose algorithm to compute the Myerson value, and a more efficient algorithm to compute the Shapley value. Since the computation of either value involves enumerating all connected induced subgraphs of the game’s underlying graph, we start by developing an algorithm dedicated to this enumeration, and then we show empirically that it is faster than the state of the art in the literature. Finally, we present a sample application of both algorithms, in which we test the Myerson value and the Shapley value as advanced measures of node centrality in networks.

PPIExp: A Web-Based Platform for Integration and Visualization of Protein-Protein Interaction Data and Spatiotemporal Proteomics Data.

Integrating spatiotemporal proteomics data with protein-protein interaction (PPI) data can help researchers make an in-depth exploration of their proteins of interest in a dynamic manner. However, there is still a lack of proper tools for the biologists who usually have few programming skills to construct a PPI network for a protein list, visualize active PPI subnetworks, and then select key nodes for further study. We propose a web-based platform named PPIExp that can automatically construct a PPI network, perform clustering analysis according to protein abundances, and perform functional enrichment analysis. More importantly, it provides multiple effective visualization interfaces, such as the interface to display the PPI network map, the interface to display a dendrogram and heatmap for the clustering result, and the interface to display the expression pattern of a selected protein. To visualize the active PPI subnetworks in specific space or time, it provides buttons to highlight the differentially expressed proteins under each condition on the network map. Additionally, to help researchers determine which proteins are worth further attention, PPIExp provides extensive one-click interactive operations to map node centrality measures to node size on the network and highlight three types of proteins, that is, the proteins in an enriched functional term, the coexpressed proteins selected from the dendgrogram and heatmap, and the proteins input by users. PPIExp is available at http://www.fgvis.com/expressvis/PPIExp .

Centrality Measures for Graphons: Accounting for Uncertainty in Networks

As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality measures rely on the assumption that the graph is perfectly known -- a premise not necessarily fulfilled for large, uncertain networks. Accordingly, centrality measures may fail to faithfully extract the importance of nodes in the presence of uncertainty. To mitigate these problems, we suggest a statistical approach based on graphon theory: we introduce formal definitions of centrality measures for graphons and establish their connections to classical graph centrality measures. A key advantage of this approach is that centrality measures defined at the modeling level of graphons are inherently robust to stochastic variations of specific graph realizations. Using the theory of linear integral operators, we define degree, eigenvector, Katz and PageRank centrality functions for graphons and establish concentration inequalities demonstrating that graphon centrality functions arise naturally as limits of their counterparts defined on sequences of graphs of increasing size. The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score. The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score.

Efficient Computation of Semivalues for Game-Theoretic Network Centrality


 
 
 Some game-theoretic solution concepts such as the Shapley value and the Banzhaf index have recently gained popularity as measures of node centrality in networks. While this direction of research is promising, the computational problems that surround it are challenging and have largely been left open. To date there are only a few positive results in the literature, which show that some game-theoretic extensions of degree-, closeness- and betweenness-centrality measures are computable in polynomial time, i.e., without the need to enumerate the exponential number of all possible coalitions. In this article, we show that these results can be extended to a much larger class of centrality measures that are based on a family of solution concepts known as semivalues. The family of semivalues includes, among others, the Shapley value and the Banzhaf index. To this end, we present a generic framework for defining game-theoretic network centralities and prove that all centrality measures that can be expressed in this framework are computable in polynomial time. Using our framework, we present a number of new and polynomial-time computable game-theoretic centrality measures.
 
 

New centrality measure for nodes based on user social status and behavior on Facebook

PurposeThis 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/approachIn 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.FindingsResults 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/valueThe 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.