基于核与核度理论的在线社交网络拓扑结构研究

项目名称： 基于核与核度理论的在线社交网络拓扑结构研究

项目编号： No.61672050

项目类型： 面上项目

立项/批准年度： 2017

项目学科： 自动化技术、计算机技术

项目作者： 李泽鹏

作者单位： 北京大学

项目金额： 32万元

中文摘要： 在线社交网络是一个复杂的巨系统，其拓扑结构的研究不仅涉及到网络的复杂性，而且与网络安全问题息息相关，是目前社交网络研究的难点。从数学角度来看，社交网络的拓扑结构就是一个复杂的图。因而，有众多学者用图论方法来研究社交网络。本项目拟将信息传播、网络安全与拓扑结构有机融为一体，通过核与核度理论对社交网络拓扑结构进行研究，其主要目标是研究社交网络社区结构以及社区与社区之间关联拓扑结构的核度最小原则属性，主要从三个方面展开：（1）利用统计分析、随机过程和图论方法建立社交网络拓扑结构模型；（2）通过引入连通中心度对影响网络连通性的节点进行筛选和排序，在此基础上设计求解核度与核心节点集的高效算法；（3）通过分析核度变化与拓扑结构变化之间的关系，探索社交网络拓扑结构的演化机理。该研究项目为在线社交网络信息传播、网络安全等研究提供了理论基础。

中文关键词： 在线社交网络；拓扑结构；模型；近似算法；核与核度理论

英文摘要： Online social network is a complex and huge system. The research on the topological structures of online social networks is a difficult problem, which is related to not only the complexity of the network, but also the security of networks. From the viewpoint of mathematics, the topological structure of an online social network is a complex graph. So, many researchers have been studying social networks from the viewpoint of graph theory. On the basis of combining organically information transmission, network security and topological structure, we study the topological structures of online social networks with core and coritivity theory. Our main goal is to study the minimum-coritivity principle of the topological structure of a community or relationship among communities. The main content includes: (1) Construct the topological structures of social networks by the methods in statistic analysis, stochastic process and graph theory; (2) Select and sort the nodes with influence to the connectivity of the network by introducing the concept of connectedness centrality, then design an efficient algorithm for finding the coritivity and core nodes of a network; (3) Explore the evolution of social networks based on the relation between the changes of coritivities and structures. This project will provide basic theories on information transmission and network security in the future.

英文关键词： Online social network;Topological structure;Model;Approximation algorithm;Core and coritivity theory