Node Importance Ranking in Complex Networks Based on Multicriteria Decision Making

In recent years, the identification of the essential nodes in complex networks has attracted significant attention because of their theoretical and practical significance in many applications, such as preventing and controlling epidemic diseases and discovering essential proteins. Several importance measures have been proposed from diverse perspectives to identify crucial nodes more accurately. In this paper, we propose a novel importance metric called node propagation entropy, which uses a combination of the clustering coefficients of nodes and the influence of the first- and second-order neighbor numbers on node importance to identify essential nodes from an entropy perspective while considering the local and global information of the network. Furthermore, the susceptible–infected–removed and susceptible–infected–removed–susceptible epidemic models along with the Kendall coefficient are used to reveal the relevant correlations among the various importance measures. The results of experiments conducted on several real networks from different domains show that the proposed metric is more accurate and stable in identifying significant nodes than many existing techniques, including degree centrality, betweenness centrality, closeness centrality, eigenvector centrality, and H-index.

Accurate measurement of important nodes in complex networks has great practical and theoretical significance. Mining important nodes should not only consider the core nodes, but also take into account the locations of the nodes in the network. Despite much research on assessing important nodes, the importance of nodes in the structural holes is still easily ignored. Therefore, a local measuring method is proposed, which evaluates the nodes importance by the total constraints caused by the lack of primary structural holes and secondary structural holes around the nodes. This method simultaneously considers both the centrality and the bridging property of the nodes' first-order and second-order neighbours. Further to prove the accuracy of the method TCM, we carry out deliberate attack simulations through selective deletion in a certain proportion of network nodes. Then, we calculate the decreased ratio of network efficiency in the before-and-after attacks. Experiment results show that the average effect of the TCM in four real networks are improved by 50.64% and 14.92% compared to the clustering coefficient index and the k-shell decomposition method, respectively. Obviously, the TCM is more accurate to mine important nodes than other two methods, and it is suitable for quantitative analysis in large-scale networks.

Betweenness centrality is a key indicator for quantifying node importance in complex networks, but remains computationally expensive for large-scale graphs due to its global dependency on all-pairs shortest paths. This research describes a machine learning-based methodology for estimating betweenness centrality with low-complexity topological features and graph neural networks. We use the GraphSAGE algorithm with two distinct neighborhood aggregation schemes- mean and max aggregator to create predictive models that generalize across unseen nodes. Four synthetic network models- Erdős- Rényi, Watts-Strogatz, Barabási-Albert, and Newman-Park are generated to evaluate generalization across diverse topologies. The experiments involve training GraphSAGE models on smaller graphs and testing on larger unseen graphs from the same topology. The Max aggregator achieves an average of approximately 3% higher Top-10 node overlap and 1% higher Spearman correlation compared to the Mean aggregator across all datasets resulting in high rank correlations and identification of most important nodes.

Identifying influential nodes in complex networks: Effective distance gravity model

Node influence ranking in complex networks: A local structure entropy approach

Centrality, which quantifies the importance of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs of nodes. Here we develop a method, based on absorbing Markov chains, that enables us to continuously interpolate both of these centrality measures away from the geodesic limit and toward a limit where no restriction is placed on the length of the paths the walkers can explore. At this second limit, the interpolated betweenness and closeness centralities reduce, respectively, to the well-known current-betweenness and resistance-closeness (information) centralities. The method is tested numerically on four real networks, revealing complex changes in node centrality rankings with respect to the value of the interpolation parameter. Nonmonotonic betweenness behaviors are found to characterize nodes that lie close to intercommunity boundaries in the studied networks.

Considering the high computational complexity of Closeness Centrality and the structural characteristics of community in complex networks, The BridgeRank (BR) algorithm to evaluate node importance of complex networks based on community division is proposed. The complex network is divided into several communities. The node with the largest local betweenness centrality in each community is extracted as the keynode of the community. The importance ranking of nodes is obtained by adopting the BR algorithm to caculate the sum of the shortest paths from each node to these key nodes in the network. The BR algorithm is achieved based on the Kernighan-Lin, Girvan-Newman, Newman fast and Louvain algorithm respectively. The experimental shows that BR algorithm based on Louvain community division has the highest accuracy in estimating node importance. On the basis that Community Size BridgeRank (CS-BR) and the Local Betweenness Centrality BridgeRank (LBC-BR) are proposed based on the size of the community and the weight of the local betweenness centrality of key nodes respectively. The experiments results on four detasets show that compared with some classic algorithms, the important nodes evaluated by the three proposed methods have stronger spread ability in SIR model, Moreover,the improved CS-BR and LBC-BR algorithm are better than BR.

Finding important nodes in complex networks is an important topic. However, the location information obtained by many previous studies is not sufficient and effective, and the types of attributes applied also have limitations. Based on K-shell and gravity model, this paper proposes a node importance measurement method based on multi-attribute fusion. In this method, the objective, comprehensive evaluation of multiple attributes is obtained by the entropy weight method. Experiments on real networks show that the proposed algorithm can effectively measure the importance of nodes.

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

Identifying important nodes in complex networks is a fundamental problem in network analysis. Although a plethora of measures has been proposed to identify important nodes in static (i.e., time-invariant) networks, there is a lack of tools in the context of temporal networks (i.e., networks whose connectivity dynamically changes over time). The aim of this paper is to propose a system-theoretic approach for identifying important nodes in temporal networks. In this direction, we first propose a generalization of the popular Katz centrality measure to the family of Markovian temporal networks using tools from the theory of Markov jump linear systems. We then show that Katz centrality in Markovian temporal networks can be efficiently computed using linear programming. Finally, we propose a convex program for optimizing the Katz centrality of a given node by tuning the weights of the temporal network in a cost-efficient manner. Numerical simulations illustrate the effectiveness of the obtained results.

Calculating centrality measures has been used to identify Cyber-physical System critical component for some time. However, accurate identification of critical elements within the interconnected system that are vulnerable to system failures and intentional attacks requires not only a reliable model but robust index to dynamic system operating environment. These measures include 1) Node Degree, 2) Node Importance, 3) Betweenness Centrality, 4) Closeness Centrality and 5) Eigenvector Centrality. System component criticalities have been evaluated based on these measures in this paper and their performances and rankings under different network topologies and operating conditions have been compared using 1) Pearson Correlation Coefficient and 2) Spearman Correlation Coefficient. This has enabled the quantification of the optimality of using different centrality measures in different network scenarios. The results suggest that Betweenness and Degree centralities are the most suitable indices for identifying critical electrical power system bus and cyber system node individually. Moreover, the degree of correlation between directed measures has suggested also the necessity of using directional model in Cyber-physical System studies.

The problem of identifying the influential spreaders - the important nodes - in a real world network is of high importance due to its theoretical interest as well as its practical applications, such as the acceleration of information diffusion, the control of the spread of a disease and the improvement of the resilience of networks to external attacks. In this paper, we propose a graph exploration sampling method that accurately identifies the influential spreaders in a complex network, without any prior knowledge of the original graph, apart from the collected samples/subgraphs. The method explores the graph, following a deterministic selection rule and outputs a graph sample - the set of edges that have been crossed. The proposed method is based on a version of Rank Degree graph sampling algorithm. We conduct extensive experiments in eight real world networks by simulating the susceptible-infected-recovered (SIR) and susceptible-infected-susceptible (SIS) epidemic models which serve as ground truth identifiers of nodes spreading efficiency. Experimentally, we show that by exploring only the 20% of the network and using the degree centrality as well as the k-core measure, we are able to identify the influential spreaders with at least the same accuracy as in the full information case, namely, the case where we have access to the original graph and in that graph, we compute the centrality measures. Finally and more importantly, we present strong evidence that the degree centrality - the degree of nodes in the collected samples - is almost as accurate as the k-core values obtained from the original graph.

Evaluating the importance of nodes in complex networks is an important topic in the research of network characteristics. Its relevant research has a wide range of applications, such as network supervision and rumor control. At present, many methods have been proposed to evaluate the importance of nodes in complex networks, but most of them have the deficiency of one-sided evaluation or too high time complexity. In order to break through the limitations of existing methods, in this paper a novel method of evaluating the importance of complex network nodes is proposed based on Tsallis entropy. This method takes into account both the local and global topological information of the node. It considers the structural hole characteristics and K-shell centrality of the node and fully takes into account the influence of the node itself and its neighboring nodes. To illustrate the effectiveness and applicability of this method, eight real networks are selected from different fields and five existing methods of evaluating node importance are used as comparison methods. On this basis, the monotonicity index, SIR (susceptible-infectious-recovered) model, and Kendall correlation coefficient are used to illustrate the superiority of this method and the relationship among different methods. Experimental results show that this method can effectively and accurately evaluate the importance of nodes in complex networks, distinguish the importance of different nodes significantly, and can show good accuracy of evaluating the node importance under different proportions of nodes. In addition, the time complexity of this method is <inline-formula><tex-math id="M2">\begin{document}$ O({n^2}) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20210979_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20210979_M2.png"/></alternatives></inline-formula>, which is suitable for large-scale complex networks.

Importance evaluation of power network nodes based on community division and characteristics of coupled network

Event Abstract Back to Event The multiplex interplay between phonological and semantic networks impacts word production across different types of aphasia Nichol Castro1* and Massimo Stella2 1 Georgia Institute of Technology, United States 2 University of Southampton, United Kingdom The structure of mental lexicon networks, where similar words are connected, influences several language processes in healthy (e.g., De Deyne, Navarro, & Storms, 2013; Vitevitch, Goldstein, Siew, & Castro, 2015) and clinical (e.g., Castro, Pelczarski, & Vitevitch, 2017) populations, above and beyond traditional psycholinguistic measures. Specific to aphasia, phonological networks were found to influence picture naming performance by people with Broca’s and Wernicke’s aphasia (Vitevitch & Castro, 2015). However, these previous endeavors only examined one type of word-word similarity (e.g., phonological similarity; Vitevitch, 2008). The more recent approach of multiplex lexical networks (Stella, Beckage, & Brede, 2017; Stella, Beckage, Brede, & De Domenico, 2018) allows consideration of semantic and phonological relationships among words simultaneously. We extend the previous analysis of picture naming by people with aphasia to include the multiplex lexical network defined in Stella et al. (2018), where words are connected on four layers representing free associations, synonyms, generalizations, and phonological similarities. We focused on three network measures, namely degree, PageRank, and closeness centrality, for each word on each layer and over the entire multiplex. Degree is a local network measure equal to the number of immediate links of a node. PageRank highlights meso-scale network patterns by identifying the most important nodes in the network. Closeness centrality is a global network measure quantifying how fast information can flow from one node to all others. As multiplex generalizations of these measures we used multidegree (the sum of word degrees across layers), PageRank versatility (De Domenico, Solé-Ribalta, Omodei, Gómez, & Arenas, 2015), and multiplex closeness centrality, respectively. To assess picture naming performance, we conducted logistic regression models predicting the probability of correct picture naming from traditional psycholinguistic predictors (word length, frequency, and age of acquisition), type of aphasia (Anomic, Conduction, Wernicke, Broca, and healthy controls), and each of the network measures (layer-specific and multiplex variants) using archival data. We found that for local and meso-structural measures (i.e. degree and PageRank), the layer-specific variants were more predictive of picture naming performance than the multiplex variants. Conversely, for the global measure of closeness centrality, we found the multiplex variant being twice more predictive of picture naming performance than layer-specific variants. Furthermore, the difference in production likelihood between words with high and low multiplex closeness centrality is considerably greater for people with different types of aphasia than healthy controls, suggesting that this measure is particularly sensitive to picture naming performance in this clinical population (Fig. 1). These findings indicate that picture naming by people with aphasia crucially depends on the global interplay between phonology and semantics, which is captured by the whole multiplex structure. These findings may have particular relevance for the treatment of aphasia. Potentially, selecting words with high multiplex closeness centrality for treatment will lead to greater generalization of treatment to untrained words than when selecting words with low closeness centrality, given that words with high multiplex closeness centrality are 1) already better accessed by people with aphasia and 2) well-connected within the entire multiplex lexical network through semantic and phonological connections. Figure 1 Acknowledgements Portions of this work were made possible with a Ruth L. Kirschstein National Research Service Award (NRSA) Institutional Research Training Grant from the National Institutes of Health (National Institute on Aging) 5T32AG000175 to NC. MS acknowledges support from a Doctoral Training Centre grant (EP/G03690X/1). References Castro, N., Pelczarski, K. M., & Vitevitch, M. S. (2017). Using Network Science Measures to Predict the Lexical Decision Performance of Adults Who Stutter. Journal of Speech, Language, and Hearing Research, 60(7), 1911-1918. De Deyne, S., Navarro, D. J., & Storms, G. (2013). Better explanations of lexical and semantic cognition using networks derived from continued rather than single-word associations.Behavior research methods, 45(2), 480-498. De Domenico, M., Solé-Ribalta, A., Omodei, E., Gómez, S., & Arenas, A. (2015). Ranking in interconnected multilayer networks reveals versatile nodes. Nature communications, 6, 6868. Stella, M., Beckage, N. M., & Brede, M. (2017). Multiplex lexical networks reveal patterns in early word acquisition in children.Scientific Reports, 7, 46730. Stella, M., Beckage, N. M., Brede, M., & De Domenico, M. (2018). Multiplex model of mental lexicon reveals explosive learning in humans. Scientific reports, 8(1), 2259. Vitevitch, M. S. (2008). What can graph theory tell us about word learning and lexical retrieval?. Journal of Speech, Language, and Hearing Research, 51(2), 408-422. Vitevitch, M. S., & Castro, N. (2015). Using network science in the language sciences and clinic. International journal of speech-language pathology, 17(1), 13-25. Vitevitch, M. S., Goldstein, R., Siew, C. S., & Castro, N. (2014). Using complex networks to understand the mental lexicon. In Yearbook of the Poznan Linguistic Meeting, 1(1), 119-138. Keywords: Aphasia, multiplex lexical networks, Psycholinguistics, complex networks, picture naming, clinical applications Conference: Academy of Aphasia 56th Annual Meeting, Montreal, Canada, 21 Oct - 23 Oct, 2018. Presentation Type: poster presentation Topic: not eligible for a student prize Citation: Castro N and Stella M (2019). The multiplex interplay between phonological and semantic networks impacts word production across different types of aphasia. Conference Abstract: Academy of Aphasia 56th Annual Meeting. doi: 10.3389/conf.fnhum.2018.228.00035 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 16 Apr 2018; Published Online: 22 Jan 2019. * Correspondence: Dr. Nichol Castro, Georgia Institute of Technology, Atlanta, United States, nichol.castro@psych.gatech.edu Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Nichol Castro Massimo Stella Google Nichol Castro Massimo Stella Google Scholar Nichol Castro Massimo Stella PubMed Nichol Castro Massimo Stella Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.