Reciprocity in social networks is a measure of information exchange between two individuals, and indicates interaction patterns between pairs of users. A recent study finds that the reciprocity coefficient of a classical directed preferential attachment (PA) model does not match empirical evidence. Towards remedying this deficiency, we extend the classical three-scenario directed PA model by adding a parameter that controls the probability of creating a reciprocal edge. This proposed model also allows edge creation between two existing nodes, making it a realistic candidate for fitting to datasets. We provide and compare two estimation procedures for fitting the new reciprocity model and demonstrate the methods on simulated and real datasets. One estimation method requires careful analysis of the heavy tail properties of the model. The fitted models provide a good match with the empirical tail distributions of both in- and out-degrees but other mismatched diagnostics suggest that further generalization of the model is warranted.
{"title":"Preferential attachment with reciprocity: properties and estimation","authors":"Daniel Cirkovic, Tiandong Wang, S. Resnick","doi":"10.1093/comnet/cnad031","DOIUrl":"https://doi.org/10.1093/comnet/cnad031","url":null,"abstract":"\u0000 Reciprocity in social networks is a measure of information exchange between two individuals, and indicates interaction patterns between pairs of users. A recent study finds that the reciprocity coefficient of a classical directed preferential attachment (PA) model does not match empirical evidence. Towards remedying this deficiency, we extend the classical three-scenario directed PA model by adding a parameter that controls the probability of creating a reciprocal edge. This proposed model also allows edge creation between two existing nodes, making it a realistic candidate for fitting to datasets. We provide and compare two estimation procedures for fitting the new reciprocity model and demonstrate the methods on simulated and real datasets. One estimation method requires careful analysis of the heavy tail properties of the model. The fitted models provide a good match with the empirical tail distributions of both in- and out-degrees but other mismatched diagnostics suggest that further generalization of the model is warranted.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"11 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2022-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60892040","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 the study of infectious diseases on networks, researchers calculate epidemic thresholds to help forecast whether or not a disease will eventually infect a large fraction of a population. Because network structure typically changes with time, which fundamentally influences the dynamics of spreading processes and in turn affects epidemic thresholds for disease propagation, it is important to examine epidemic thresholds in models of disease spread on temporal networks. Most existing studies of epidemic thresholds in temporal networks have focused on models in discrete time, but most real-world networked systems evolve continuously with time. In our work, we encode the continuous time-dependence of networks in the evaluation of the epidemic threshold of a susceptible–infected–susceptible (SIS) process by studying an SIS model on tie-decay networks. We derive the epidemic-threshold condition of this model, and we perform numerical experiments to verify it. We also examine how different factors—the decay coefficients of the tie strengths in a network, the frequency of the interactions between the nodes in the network, and the sparsity of the underlying social network on which interactions occur—lead to decreases or increases of the critical values of the threshold and hence contribute to facilitating or impeding the spread of a disease. We thereby demonstrate how the features of tie-decay networks alter the outcome of disease spread.
{"title":"Epidemic thresholds of infectious diseases on tie-decay networks","authors":"Qinyi Chen;Mason A Porter;Naoki Masuda","doi":"10.1093/comnet/cnab031","DOIUrl":"https://doi.org/10.1093/comnet/cnab031","url":null,"abstract":"In the study of infectious diseases on networks, researchers calculate epidemic thresholds to help forecast whether or not a disease will eventually infect a large fraction of a population. Because network structure typically changes with time, which fundamentally influences the dynamics of spreading processes and in turn affects epidemic thresholds for disease propagation, it is important to examine epidemic thresholds in models of disease spread on temporal networks. Most existing studies of epidemic thresholds in temporal networks have focused on models in discrete time, but most real-world networked systems evolve continuously with time. In our work, we encode the continuous time-dependence of networks in the evaluation of the epidemic threshold of a susceptible–infected–susceptible (SIS) process by studying an SIS model on tie-decay networks. We derive the epidemic-threshold condition of this model, and we perform numerical experiments to verify it. We also examine how different factors—the decay coefficients of the tie strengths in a network, the frequency of the interactions between the nodes in the network, and the sparsity of the underlying social network on which interactions occur—lead to decreases or increases of the critical values of the threshold and hence contribute to facilitating or impeding the spread of a disease. We thereby demonstrate how the features of tie-decay networks alter the outcome of disease spread.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 1","pages":"1-24"},"PeriodicalIF":2.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49961865","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}
The efficiency of the international oil trade networks (iOTNs) is an important measure of the efficient redistribution of oil resources among various economies. Adopting cooperation strategies between economies can enhance the efficiency of the iOTNs. We design a series of trade cooperation strategies based on trade volumes, geographic locations and local similarities of economies, and quantitatively analyse the impact of new trade relations on the efficiency of the iOTNs under different trade cooperation strategies. We find that the oil trade system rapidly developed into a more efficient system for the flows of resources and market information. When the proportion of newly added trade relationships is fairly large, the win–win strategy can improve the network efficiency the most; otherwise, the common neighbour strategy performs the best.
{"title":"The performance of cooperation strategies for enhancing the efficiency of international oil trade networks","authors":"Na Wei;Wen-Jie Xie;Wei-Xing Zhou;Naoki Masuda","doi":"10.1093/comnet/cnab053","DOIUrl":"https://doi.org/10.1093/comnet/cnab053","url":null,"abstract":"The efficiency of the international oil trade networks (iOTNs) is an important measure of the efficient redistribution of oil resources among various economies. Adopting cooperation strategies between economies can enhance the efficiency of the iOTNs. We design a series of trade cooperation strategies based on trade volumes, geographic locations and local similarities of economies, and quantitatively analyse the impact of new trade relations on the efficiency of the iOTNs under different trade cooperation strategies. We find that the oil trade system rapidly developed into a more efficient system for the flows of resources and market information. When the proportion of newly added trade relationships is fairly large, the win–win strategy can improve the network efficiency the most; otherwise, the common neighbour strategy performs the best.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 1","pages":"1-18"},"PeriodicalIF":2.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49961869","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}
Su Yuan Chan;Kerri Morgan;Nicholas Parsons;Julien Ugon;Jonathan Crofts
In this article, we present two new concepts related to subgraph counting where the focus is not on the number of subgraphs that are isomorphic to some fixed graph $H$ , but on the frequency with which a vertex or an edge belongs to such subgraphs. In particular, we are interested in the case where $H$ is a complete graph. These new concepts are termed vertex participation and edge participation, respectively. We combine these concepts with that of the rich-club to identify what we call a Super rich-club and rich edge-club. We show that the concept of vertex participation is a generalization of the rich-club. We present experimental results on randomized Erdös–Rényi and Watts–Strogatz small-world networks. We further demonstrate both concepts on a complex brain network and compare our results to the rich-club of the brain.
{"title":"Supernodes: a generalization of the rich-club","authors":"Su Yuan Chan;Kerri Morgan;Nicholas Parsons;Julien Ugon;Jonathan Crofts","doi":"10.1093/comnet/cnab052","DOIUrl":"https://doi.org/10.1093/comnet/cnab052","url":null,"abstract":"In this article, we present two new concepts related to subgraph counting where the focus is not on the number of subgraphs that are isomorphic to some fixed graph \u0000<tex>$H$</tex>\u0000, but on the frequency with which a vertex or an edge belongs to such subgraphs. In particular, we are interested in the case where \u0000<tex>$H$</tex>\u0000 is a complete graph. These new concepts are termed vertex participation and edge participation, respectively. We combine these concepts with that of the rich-club to identify what we call a Super rich-club and rich edge-club. We show that the concept of vertex participation is a generalization of the rich-club. We present experimental results on randomized Erdös–Rényi and Watts–Strogatz small-world networks. We further demonstrate both concepts on a complex brain network and compare our results to the rich-club of the brain.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 1","pages":"1-18"},"PeriodicalIF":2.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49980811","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}
{"title":"Corrigendum to: Multivariate Hawkes process analysis of posts on a web service about uncomfortable gender experiences","authors":"Masatoshi Goda;Ryosuke Yano;Takayuki Mizuno;Tiago Pereira","doi":"10.1093/comnet/cnab015","DOIUrl":"https://doi.org/10.1093/comnet/cnab015","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 1","pages":"1-1"},"PeriodicalIF":2.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49961870","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}
Embodied and intersubjective experience is crucial to the social cognition processes on which interpersonal relationships are based. We assessed whether promoting these processes through participation in self-awareness and empathic interaction activities can influence social integration among peers in 7- to 8-year-old children. The intervention, conducted in a school context, included mindfulness-based practices (favouring self-awareness), empathic collaboration activities and perspective-taking instances (promoting other-oriented awareness). To evaluate social integration levels, children were asked to complete a sociometric questionnaire, each listing the peers they would choose to play with (positive ties) and those they would prefer not to play with (negative ties). Based on this relational data, two types of directed networks were constructed: positive networks (PN) and negative networks (NN), in two temporal instances (pre- and post-intervention). In both the experimental and waitlist groups, pre–post intervention changes in the topology of peer social networks were evaluated by analysing global network properties such as connectivity, degree distribution, density, reciprocity, transitivity and modular structure. Our findings showed that after participating in the intervention social integration was improved, reflected in increased general interconnection of positive ties: greater average connectivity and density in PN, more equitably distributed choices (no evident leadership), greater cohesion and an increase in the number of reciprocal interactions. Additionally, we found a lower level of social rejection; that is, lower average connectivity and density in NN, the persistence of only mutual negative choices and negative ties confined to small groups. These findings were not observed in the waitlist group. This study demonstrates how participation in an intervention that promotes social cognition processes can influence the structure of peer social networks, favouring social integration. The social network analysis provides quantitative evidence of the plasticity of social relationships in children, constituting a valuable tool for the assessment of this kind of intervention at a group level.
{"title":"Social relationships in children: favourable influence of activities promoting self-awareness and empathic interaction","authors":"Natalia Carro;Marcelo Kuperman;Paola D'adamo;Mariana Lozada;Johann Martinez","doi":"10.1093/comnet/cnab049","DOIUrl":"https://doi.org/10.1093/comnet/cnab049","url":null,"abstract":"Embodied and intersubjective experience is crucial to the social cognition processes on which interpersonal relationships are based. We assessed whether promoting these processes through participation in self-awareness and empathic interaction activities can influence social integration among peers in 7- to 8-year-old children. The intervention, conducted in a school context, included mindfulness-based practices (favouring self-awareness), empathic collaboration activities and perspective-taking instances (promoting other-oriented awareness). To evaluate social integration levels, children were asked to complete a sociometric questionnaire, each listing the peers they would choose to play with (positive ties) and those they would prefer not to play with (negative ties). Based on this relational data, two types of directed networks were constructed: positive networks (PN) and negative networks (NN), in two temporal instances (pre- and post-intervention). In both the experimental and waitlist groups, pre–post intervention changes in the topology of peer social networks were evaluated by analysing global network properties such as connectivity, degree distribution, density, reciprocity, transitivity and modular structure. Our findings showed that after participating in the intervention social integration was improved, reflected in increased general interconnection of positive ties: greater average connectivity and density in PN, more equitably distributed choices (no evident leadership), greater cohesion and an increase in the number of reciprocal interactions. Additionally, we found a lower level of social rejection; that is, lower average connectivity and density in NN, the persistence of only mutual negative choices and negative ties confined to small groups. These findings were not observed in the waitlist group. This study demonstrates how participation in an intervention that promotes social cognition processes can influence the structure of peer social networks, favouring social integration. The social network analysis provides quantitative evidence of the plasticity of social relationships in children, constituting a valuable tool for the assessment of this kind of intervention at a group level.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 1","pages":"1-15"},"PeriodicalIF":2.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49980814","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 : 2022-01-01DOI: 10.1016/j.jco.2022.101649
A. Vasil'eva
{"title":"Kolmogorov widths of intersections of finite-dimensional balls","authors":"A. Vasil'eva","doi":"10.1016/j.jco.2022.101649","DOIUrl":"https://doi.org/10.1016/j.jco.2022.101649","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"25 1","pages":"101649"},"PeriodicalIF":2.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73467620","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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