Complex network is an important tool for studying complex systems. From the mesoscopic perspective, the complex network is composed of a large number of different types of motifs, research on the importance of motifs is helpful to analyse the function and dynamics of a complex network. However, the importance of different motifs or the same kind of motifs in the network is different, and the importance of motifs is not only affected by a single factor. Therefore, we propose a comprehensive measurement method of motif importance based on multi-attribute decision-making (MAM). We use the idea of MAM and take into account the influence of the local attribute, global attribute and location attribute of the motif on the network structure and function, and the information entropy method is used to give different weight to different attributes, finally, a comprehensive importance measure of the motif is obtained. Experimental results on the artificial network and real networks show that our method is more direct and effective for a small network.
{"title":"Motif importance measurement based on multi-attribute decision","authors":"Biao Feng;Yunyun Yang;Liao Zhang;Shuhong Xue;Xinlin Xie;Jiianrong Wang;Gang Xie","doi":"10.1093/comnet/cnac023","DOIUrl":"https://doi.org/10.1093/comnet/cnac023","url":null,"abstract":"Complex network is an important tool for studying complex systems. From the mesoscopic perspective, the complex network is composed of a large number of different types of motifs, research on the importance of motifs is helpful to analyse the function and dynamics of a complex network. However, the importance of different motifs or the same kind of motifs in the network is different, and the importance of motifs is not only affected by a single factor. Therefore, we propose a comprehensive measurement method of motif importance based on multi-attribute decision-making (MAM). We use the idea of MAM and take into account the influence of the local attribute, global attribute and location attribute of the motif on the network structure and function, and the information entropy method is used to give different weight to different attributes, finally, a comprehensive importance measure of the motif is obtained. Experimental results on the artificial network and real networks show that our method is more direct and effective for a small network.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we propose a method to reconstruct the active links of a power network described by a second-order Kuramoto model and subject to dynamically induced cascading failures. Starting from the assumption (realistic for power grids) that the structure of the network is known, our method reconstructs the active links from the evolution of the relevant dynamical quantities of the nodes of the system, that is, the node phases and angular velocities. We find that, to reconstruct the temporal sequence of the faults, it is crucial to use time series with a small number of samples, as the observation window should be smaller than the temporal distance between subsequent events. This requirement is in contrast with the need of using larger sets of data in the presence of noise, such that the number of samples to feed in the algorithm has to be selected as a trade-off between the prediction error and temporal resolution of the active link reconstruction.
{"title":"Reconstruction of cascading failures in dynamical models of power grids","authors":"Alessandra Corso;Lucia Valentina Gambuzza;Federico Malizia;Giovanni Russo;Vito Latora;Mattia Frasca","doi":"10.1093/comnet/cnac035","DOIUrl":"https://doi.org/10.1093/comnet/cnac035","url":null,"abstract":"In this article, we propose a method to reconstruct the active links of a power network described by a second-order Kuramoto model and subject to dynamically induced cascading failures. Starting from the assumption (realistic for power grids) that the structure of the network is known, our method reconstructs the active links from the evolution of the relevant dynamical quantities of the nodes of the system, that is, the node phases and angular velocities. We find that, to reconstruct the temporal sequence of the faults, it is crucial to use time series with a small number of samples, as the observation window should be smaller than the temporal distance between subsequent events. This requirement is in contrast with the need of using larger sets of data in the presence of noise, such that the number of samples to feed in the algorithm has to be selected as a trade-off between the prediction error and temporal resolution of the active link reconstruction.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Graph embedding is a transformation of nodes of a graph into a set of vectors. A good embedding should capture the graph topology, node-to-node relationship and other relevant information about the graph, its subgraphs and nodes. If these objectives are achieved, an embedding is a meaningful, understandable, compressed representations of a network that can be used for other machine learning tools such as node classification, community detection or link prediction. In this article, we do a series of extensive experiments with selected graph embedding algorithms, both on real-world networks as well as artificially generated ones. Based on those experiments, we formulate the following general conclusions. First, we confirm the main problem of node embeddings that is rather well-known to practitioners but less documented in the literature. There exist many algorithms available to choose from which use different techniques and have various parameters that may be tuned, the dimension being one of them. One needs to ensure that embeddings describe the properties of the underlying graphs well but, as our experiments confirm, it highly depends on properties of the network at hand and the given application in mind. As a result, selecting the best embedding is a challenging task and very often requires domain experts. Since investigating embeddings in a supervised manner is computationally expensive, there is a need for an unsupervised tool that is able to select a handful of promising embeddings for future (supervised) investigation. A general framework, introduced recently in the literature and easily available on GitHub repository, provides one of the very first tools for an unsupervised graph embedding comparison by assigning the ‘divergence score’ to embeddings with a goal of distinguishing good from bad ones. We show that the divergence score strongly correlates with the quality of embeddings by investigating three main applications of node embeddings: node classification, community detection and link prediction.
{"title":"Evaluating node embeddings of complex networks","authors":"Arash Dehghan-Kooshkghazi;Bogumił Kamiński;Łukasz Kraiński;Paweł Prałat;François Théberge;Ali Pinar","doi":"10.1093/comnet/cnac030","DOIUrl":"https://doi.org/10.1093/comnet/cnac030","url":null,"abstract":"Graph embedding is a transformation of nodes of a graph into a set of vectors. A good embedding should capture the graph topology, node-to-node relationship and other relevant information about the graph, its subgraphs and nodes. If these objectives are achieved, an embedding is a meaningful, understandable, compressed representations of a network that can be used for other machine learning tools such as node classification, community detection or link prediction. In this article, we do a series of extensive experiments with selected graph embedding algorithms, both on real-world networks as well as artificially generated ones. Based on those experiments, we formulate the following general conclusions. First, we confirm the main problem of node embeddings that is rather well-known to practitioners but less documented in the literature. There exist many algorithms available to choose from which use different techniques and have various parameters that may be tuned, the dimension being one of them. One needs to ensure that embeddings describe the properties of the underlying graphs well but, as our experiments confirm, it highly depends on properties of the network at hand and the given application in mind. As a result, selecting the best embedding is a challenging task and very often requires domain experts. Since investigating embeddings in a supervised manner is computationally expensive, there is a need for an unsupervised tool that is able to select a handful of promising embeddings for future (supervised) investigation. A general framework, introduced recently in the literature and easily available on GitHub repository, provides one of the very first tools for an unsupervised graph embedding comparison by assigning the ‘divergence score’ to embeddings with a goal of distinguishing good from bad ones. We show that the divergence score strongly correlates with the quality of embeddings by investigating three main applications of node embeddings: node classification, community detection and link prediction.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Betweenness centrality (BC) is a measure of the importance of a vertex in a graph, which is defined using the number of the shortest paths passing through the vertex. Brandes proposed an efficient algorithm for computing the BC scores of all vertices in a graph, which accumulates pair dependencies while traversing single-source shortest paths. Although this algorithm works well on static graphs, its direct application to dynamic graphs takes a huge amount of computation time because the BC scores must be computed from scratch every time the structure of graph changes. Therefore, various algorithms for updating the BC scores of all vertices have been developed so far. In this article, we propose a novel algorithm for updating the BC scores of all vertices in a graph upon deletion of a single edge. We also show the validity and efficiency of the proposed algorithm through theoretical analysis and experiments using various graphs obtained from synthetic and real networks.
{"title":"An algorithm for updating betweenness centrality scores of all vertices in a graph upon deletion of a single edge","authors":"Yoshiki Satotani;Tsuyoshi Migita;Norikazu Takahashi;Ernesto Estrada","doi":"10.1093/comnet/cnac033","DOIUrl":"https://doi.org/10.1093/comnet/cnac033","url":null,"abstract":"Betweenness centrality (BC) is a measure of the importance of a vertex in a graph, which is defined using the number of the shortest paths passing through the vertex. Brandes proposed an efficient algorithm for computing the BC scores of all vertices in a graph, which accumulates pair dependencies while traversing single-source shortest paths. Although this algorithm works well on static graphs, its direct application to dynamic graphs takes a huge amount of computation time because the BC scores must be computed from scratch every time the structure of graph changes. Therefore, various algorithms for updating the BC scores of all vertices have been developed so far. In this article, we propose a novel algorithm for updating the BC scores of all vertices in a graph upon deletion of a single edge. We also show the validity and efficiency of the proposed algorithm through theoretical analysis and experiments using various graphs obtained from synthetic and real networks.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016804/10070447/10070457.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Trust and reputation are a person's belief over another person and are essential factors while opinion values are shared among online social platforms. Both the values are calculated using past shared opinions and the structure of the network. Further, a credibility score is calculated using the trust and reputation of the nodes, which is helpful to share the opinion values more accurately. In this work, an opinion dynamics temporal network is modelled using the credibility score of the nodes in the network. The addition and deletion of the edges and the opinion evolution occur on the basis of the credibility score of the nodes. Results are analysed over scale-free networks generated using Bollabas et al. model. Such scale-free networks are evolved over time termed as temporal network using the proposed model. It is analysed how the different threshold values on the credibility score of the nodes affect the opinion values convergence on the proposed model.
{"title":"Trust- and reputation-based opinion dynamics modelling over temporal networks","authors":"Eeti Jain;Anurag Singh;Ernesto Estrada","doi":"10.1093/comnet/cnac019","DOIUrl":"https://doi.org/10.1093/comnet/cnac019","url":null,"abstract":"Trust and reputation are a person's belief over another person and are essential factors while opinion values are shared among online social platforms. Both the values are calculated using past shared opinions and the structure of the network. Further, a credibility score is calculated using the trust and reputation of the nodes, which is helpful to share the opinion values more accurately. In this work, an opinion dynamics temporal network is modelled using the credibility score of the nodes in the network. The addition and deletion of the edges and the opinion evolution occur on the basis of the credibility score of the nodes. Results are analysed over scale-free networks generated using Bollabas et al. model. Such scale-free networks are evolved over time termed as temporal network using the proposed model. It is analysed how the different threshold values on the credibility score of the nodes affect the opinion values convergence on the proposed model.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-01DOI: 10.1016/j.jco.2022.101680
Jia Chen
{"title":"EC-(t1, t2)-tractability of approximation in weighted Korobov spaces in the worst case setting","authors":"Jia Chen","doi":"10.1016/j.jco.2022.101680","DOIUrl":"https://doi.org/10.1016/j.jco.2022.101680","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78608191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-01DOI: 10.1016/j.jco.2022.101679
S. Dong, Wenchang Sun
{"title":"Learning rate of distribution regression with dependent samples","authors":"S. Dong, Wenchang Sun","doi":"10.1016/j.jco.2022.101679","DOIUrl":"https://doi.org/10.1016/j.jco.2022.101679","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81030457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-01DOI: 10.1016/j.jco.2022.101678
I. Argyros, S. George, Christoper Argyros
{"title":"On the complexity of convergence for high order iterative methods","authors":"I. Argyros, S. George, Christoper Argyros","doi":"10.1016/j.jco.2022.101678","DOIUrl":"https://doi.org/10.1016/j.jco.2022.101678","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82115245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-01DOI: 10.1016/j.jco.2022.101669
Eric Novak
{"title":"Announcement: IBC award 2022 and the nomination deadline 2023","authors":"Eric Novak","doi":"10.1016/j.jco.2022.101669","DOIUrl":"https://doi.org/10.1016/j.jco.2022.101669","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79558504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Math anxiety is a clinical pathology impairing cognitive processing in math-related contexts. Originally thought to affect only inexperienced, low-achieving students, recent investigations show how math anxiety is vastly diffused even among high-performing learners. This review of data-informed studies outlines math anxiety as a complex system that: (i) cripples well-being, self-confidence and information processing on both conscious and subconscious levels, (ii) can be transmitted by social interactions, like a pathogen, and worsened by distorted perceptions, (iii) affects roughly 20$%$ of students in 63 out of 64 worldwide educational systems but correlates weakly with academic performance and (iv) poses a concrete threat to students’ well-being, computational literacy and career prospects in science. These patterns underline the crucial need to go beyond performance for estimating math anxiety. Recent advances in network psychometrics and cognitive network science provide ideal frameworks for detecting, interpreting and intervening upon such clinical condition. Merging education research, psychology and data science, the approaches reviewed here reconstruct psychological constructs as complex systems, represented either as multivariate correlation models (e.g. graph exploratory analysis) or as cognitive networks of semantic/emotional associations (e.g. free association networks or forma mentis networks). Not only can these interconnected networks detect otherwise hidden levels of math anxiety but—more crucially—they can unveil the specific layout of interacting factors, for example, key sources and targets, behind math anxiety in a given cohort. As discussed here, these network approaches open concrete ways for unveiling students’ perceptions, emotions and mental well-being, and can enable future powerful data-informed interventions untangling math anxiety.
{"title":"A fast parameter estimator for large complex networks","authors":"Grover E. C. Guzman, D. Takahashi, André Fujita","doi":"10.1093/comnet/cnac022","DOIUrl":"https://doi.org/10.1093/comnet/cnac022","url":null,"abstract":"\u0000 Math anxiety is a clinical pathology impairing cognitive processing in math-related contexts. Originally thought to affect only inexperienced, low-achieving students, recent investigations show how math anxiety is vastly diffused even among high-performing learners. This review of data-informed studies outlines math anxiety as a complex system that: (i) cripples well-being, self-confidence and information processing on both conscious and subconscious levels, (ii) can be transmitted by social interactions, like a pathogen, and worsened by distorted perceptions, (iii) affects roughly 20$%$ of students in 63 out of 64 worldwide educational systems but correlates weakly with academic performance and (iv) poses a concrete threat to students’ well-being, computational literacy and career prospects in science. These patterns underline the crucial need to go beyond performance for estimating math anxiety. Recent advances in network psychometrics and cognitive network science provide ideal frameworks for detecting, interpreting and intervening upon such clinical condition. Merging education research, psychology and data science, the approaches reviewed here reconstruct psychological constructs as complex systems, represented either as multivariate correlation models (e.g. graph exploratory analysis) or as cognitive networks of semantic/emotional associations (e.g. free association networks or forma mentis networks). Not only can these interconnected networks detect otherwise hidden levels of math anxiety but—more crucially—they can unveil the specific layout of interacting factors, for example, key sources and targets, behind math anxiety in a given cohort. As discussed here, these network approaches open concrete ways for unveiling students’ perceptions, emotions and mental well-being, and can enable future powerful data-informed interventions untangling math anxiety.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84774369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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