Study On The Stability Of Social Networks Based On Network Structure

In recent years, with the rapid development of the online social networks, network stability has become a most attractive subject. There exists a universal phenomenon named "network collapse" in social networks:each user will leave because of his friends leaving, thus cause other friends leaving, which lead to a cascade decrease even disintegration in the number of users in the network gradually. Therefore how to effectively control and reduce the "network collapse" phenomenon has been a key problem in the practice and research.The main works in this article as follows:Firstly, in view of the above phenomenon, this article proposes the k-core model (the Tolerance K-core Problem, TKP) based on the pre-existing the Anchored K-core Problem(AKP) model. Nodes with tolerance can tolerate the number of friends be below a set threshold k, whereas will not be for ever reserved in networks like anchors. Compared with the AKP model, TKP model can describe user’s response to network collapsed in more detail, thus imitating the process of actual social network collapse more precisely, and analyzing the effect of invulnerability mechanism much better.Secondly, this article analyzes how tolerance affect network collapse in the TKP model and. how tolerance works in different networks. Compared with the AKP model, the TKP model can effectively prevent network collapse at a very small expense. We can change the threshold in the TKP model and can effectively distinguish which tolerance can keep the network more stable.In the process of tolerance proportion selection increasing from0to1, there all exist a threshold which makes the number of k-core become large suddenly in ER, WS and BA networks. What’s more, the larger the tolerance is, the smaller the threshold will be. In addition, compared with ER and WS network, the change of k-core nodes’number is more stable in BA network.Thirdly, this article will compare the effect of different selection strategy of tolerance nodes in preventing network collapse. Select strategies in tolerance nodes:the largest degree node-based priority selected, the highest betweenness node-base priority selected, the highest shell node-base priority selected and random selected of four strategies, the highest shell node-base priority selected strategy is superior to other strategies, but the effect is not as good as the highest betweenness node-base priority selected and the largest degree node-based priority selected than randomly selected.In conclusion we verify that the TKP model can effectively help keep the network more stable since its adjustment to the proportion of node selected with tolerance and network selection strategies according to networks with different characteristics.