A novel Markovian network evolution model is introduced and analysed by means of information theory. It will be proved that the model, called network evolution chain, is a stationary and ergodic stochastic process. Therefore, the asymptotic equipartition property can be applied to it. The model’s entropy rate and typical sequences are also explored. Extracting particular information from the network and methods to simulate network evolution in the continuous time domain are discussed. Additionally, the Erdős–Rényi network evolution chain is introduced as a subset of our model with the additional property of its stationary distribution matching the Erdős–Rényi random graph model. The stationary distributions of nodes and graphs are calculated for this subset alongside its entropy rate. The simulation results at the end of the article back up the proved theorems and calculated values.
{"title":"An Information Theory Approach to Network Evolution Models","authors":"Amirmohammad Farzaneh, J. Coon","doi":"10.1093/comnet/cnac020","DOIUrl":"https://doi.org/10.1093/comnet/cnac020","url":null,"abstract":"\u0000 A novel Markovian network evolution model is introduced and analysed by means of information theory. It will be proved that the model, called network evolution chain, is a stationary and ergodic stochastic process. Therefore, the asymptotic equipartition property can be applied to it. The model’s entropy rate and typical sequences are also explored. Extracting particular information from the network and methods to simulate network evolution in the continuous time domain are discussed. Additionally, the Erdős–Rényi network evolution chain is introduced as a subset of our model with the additional property of its stationary distribution matching the Erdős–Rényi random graph model. The stationary distributions of nodes and graphs are calculated for this subset alongside its entropy rate. The simulation results at the end of the article back up the proved theorems and calculated values.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89780720","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 : 2022-01-18DOI: 10.1016/j.jco.2022.101691
Jiansong Li, Heping Wang
{"title":"Optimal randomized quadrature for weighted Sobolev and Besov classes with the Jacobi weight on the ball","authors":"Jiansong Li, Heping Wang","doi":"10.1016/j.jco.2022.101691","DOIUrl":"https://doi.org/10.1016/j.jco.2022.101691","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85764277","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}
One of the most effective strategies to mitigate the global spreading of a pandemic (e.g. coronavirus disease 2019) is to shut down international airports. From a network theory perspective, this is since international airports and flights, essentially playing the roles of bridge nodes and bridge links between countries as individual communities, dominate the epidemic spreading characteristics in the whole multi-community system. Among all epidemic characteristics, the peak fraction of infected, $I_{max}$, is a decisive factor in evaluating an epidemic strategy given limited capacity of medical resources but is seldom considered in multi-community models. In this article, we study a general two-community system interconnected by a fraction $r$ of bridge nodes and its dynamic properties, especially $I_{max}$, under the evolution of the susceptible-infected-recovered model. Comparing the characteristic time scales of different parts of the system allows us to analytically derive the asymptotic behaviour of $I_{max}$ with $r$, as $rrightarrow 0$, which follows different power-law relations in each regime of the phase diagram. We also detect crossovers when $I_{max}$ changes from one power law to another, crossing different power-law regimes as driven by $r$. Our results enable a better prediction of the effectiveness of strategies acting on bridge nodes, denoted by the power-law exponent $epsilon_I$ as in $I_{max}propto r^{1/epsilon_I}$.
{"title":"Peak fraction of infected in epidemic spreading for multi-community networks","authors":"Jing Ma, Xiangyi Meng, L. Braunstein","doi":"10.1093/comnet/cnac021","DOIUrl":"https://doi.org/10.1093/comnet/cnac021","url":null,"abstract":"\u0000 One of the most effective strategies to mitigate the global spreading of a pandemic (e.g. coronavirus disease 2019) is to shut down international airports. From a network theory perspective, this is since international airports and flights, essentially playing the roles of bridge nodes and bridge links between countries as individual communities, dominate the epidemic spreading characteristics in the whole multi-community system. Among all epidemic characteristics, the peak fraction of infected, $I_{max}$, is a decisive factor in evaluating an epidemic strategy given limited capacity of medical resources but is seldom considered in multi-community models. In this article, we study a general two-community system interconnected by a fraction $r$ of bridge nodes and its dynamic properties, especially $I_{max}$, under the evolution of the susceptible-infected-recovered model. Comparing the characteristic time scales of different parts of the system allows us to analytically derive the asymptotic behaviour of $I_{max}$ with $r$, as $rrightarrow 0$, which follows different power-law relations in each regime of the phase diagram. We also detect crossovers when $I_{max}$ changes from one power law to another, crossing different power-law regimes as driven by $r$. Our results enable a better prediction of the effectiveness of strategies acting on bridge nodes, denoted by the power-law exponent $epsilon_I$ as in $I_{max}propto r^{1/epsilon_I}$.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76205256","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}
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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