{"title":"动态图控制的流方程在社交网络分析中的应用","authors":"Falciani, S ́anchez P ́erez","doi":"10.32523/2306-6172-2023-11-1-79-97","DOIUrl":null,"url":null,"abstract":"Consider a model of information propagation through a network based on time- dependent directed graphs. Let us consider a pulse that starts at any node and an index—a real function acting on the nodes of the network—that represents the state of a node with respect to the transit of this signal. We present a flow-type equation to be satisfied by these indices, which allows us to unify the method for writing the mathematical formulas describing their evolution, and also to define new indices for global evaluation of the information circulation process. We focus our attention on the dissemination of information through Twitter, showing that PageRank is a basic example of index satisfying the flow equation, and also that we can use the flow equation to generate new meaningful indices in a constructive way.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A FLOW EQUATION FOR DYNAMIC GRAPH CONTROL: APPLICATIONS TO SOCIAL NETWORK ANALYSIS\",\"authors\":\"Falciani, S ́anchez P ́erez\",\"doi\":\"10.32523/2306-6172-2023-11-1-79-97\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consider a model of information propagation through a network based on time- dependent directed graphs. Let us consider a pulse that starts at any node and an index—a real function acting on the nodes of the network—that represents the state of a node with respect to the transit of this signal. We present a flow-type equation to be satisfied by these indices, which allows us to unify the method for writing the mathematical formulas describing their evolution, and also to define new indices for global evaluation of the information circulation process. We focus our attention on the dissemination of information through Twitter, showing that PageRank is a basic example of index satisfying the flow equation, and also that we can use the flow equation to generate new meaningful indices in a constructive way.\",\"PeriodicalId\":42910,\"journal\":{\"name\":\"Eurasian Journal of Mathematical and Computer Applications\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Eurasian Journal of Mathematical and Computer Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32523/2306-6172-2023-11-1-79-97\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Eurasian Journal of Mathematical and Computer Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32523/2306-6172-2023-11-1-79-97","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
A FLOW EQUATION FOR DYNAMIC GRAPH CONTROL: APPLICATIONS TO SOCIAL NETWORK ANALYSIS
Consider a model of information propagation through a network based on time- dependent directed graphs. Let us consider a pulse that starts at any node and an index—a real function acting on the nodes of the network—that represents the state of a node with respect to the transit of this signal. We present a flow-type equation to be satisfied by these indices, which allows us to unify the method for writing the mathematical formulas describing their evolution, and also to define new indices for global evaluation of the information circulation process. We focus our attention on the dissemination of information through Twitter, showing that PageRank is a basic example of index satisfying the flow equation, and also that we can use the flow equation to generate new meaningful indices in a constructive way.
期刊介绍：
Eurasian Journal of Mathematical and Computer Applications (EJMCA) publishes carefully selected original research papers in all areas of Applied mathematics first of all from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time Eurasian Journal of Mathematical and Computer Applications (EJMCA) will also publish survey papers. Eurasian Mathematical Journal publishes 4 issues in a year. A working language of the journal is English. Main topics are: - Mathematical methods and modeling in mechanics, mining, biology, geophysics, electrodynamics, acoustics, industry. - Inverse problems of mathematical physics: theory and computational approaches. - Medical and industry tomography. - Computer applications: distributed information systems, decision-making systems, embedded systems, information security, graphics.
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