Towards Structural Stability of Social Networks

The structural stability of a social network indicates the ability of the network to maintain a sustainable service, which is important for both the network holders and the participants. Graphs are widely used to model social networks, where the coreness of a vertex (node) has been validated as the "best practice" for capturing a user's engagement. Based on this argument, we study the following problems: 1) reinforcing the network structural stability by detecting critical users, with its efficient solution in distributed computation environment; 2) monitoring each user's influence on the network structural stability. Firstly, we aim to reinforce a social network in a global manner, instead of focusing on a local view as existing works, e.g., the anchored k-core problem aims to enlarge the size of k-core with a fixed input k. We propose a new model so-called the anchored coreness problem: anchoring a small number of users to maximize the coreness gain (the total increment of coreness) of all the users in the network. We prove the problem is NP-hard and show it is more challenging than the existing local-view problems. An efficient greedy algorithm is proposed with novel techniques on pruning search space and reusing the intermediate results. The algorithm is also extended to distributed environment with a novel graph partition strategy to ensure the computing independency of each machine. Extensive experiments on real-life data demonstrate that our model is effective for reinforcing social networks and our algorithms are efficient. Secondly, although the static engagement of a user is well estimated by its coreness, each user's influence on other users is not well monitored when its engagement is weakened or strengthened. Besides, the dynamic of user engagement has not been well captured for evolving networks. We systematically study the network dynamic against the engagement change of each user. The influence of a user is monitored via two novel concepts: the collapsed power to measure the effect of user weakening, and the anchored power to measure the effect of user strengthening. The two concepts can be naturally integrated such that a unified offline algorithm is proposed to compute both the collapsed and anchored followers for each user. When the network structure evolves, online techniques are designed to maintain the users' followers, which is faster than redoing the offline algorithm by around 3 orders of magnitude