Rong-Hua Li

Efficient Core Maintenance in Large Dynamic Graphs

The k-core decomposition in a graph is a fundamental problem for social network analysis. The problem of k-core decomposition is to calculate the core number for every node in a graph. Previous studies mainly focus on k-core decomposition in a static graph. There exists a linear time algorithm for k-core decomposition in a static graph. However, in many real-world applications such as online social networks and the Internet, the graph typically evolves overtime. In such applications, a key issue is to maintain the core numbers of nodes when the graph changes overtime. A simple implementation is to perform the linear time algorithm to recompute the core number for every node after the graph is updated. Such simple implementation is expensive when the graph is very large. In this paper, we propose a new efficient algorithm to maintain the core number for every node in a dynamic graph. Our main result is that only certain nodes need to update their core numbers when the graph is changed by inserting/deleting an edge. We devise an efficient algorithm to identify and recompute the core numbers of such nodes. The complexity of our algorithm is independent of the graph size. In addition, to further accelerate the algorithm, we develop two pruning strategies by exploiting the lower and upper bounds of the core number. Finally, we conduct extensive experiments over both real-world and synthetic datasets, and the results demonstrate the efficiency of the proposed algorithm.

Influential community search in large networks

Community search is a problem of finding densely connected subgraphs that satisfy the query conditions in a network, which has attracted much attention in recent years. However, all the previous studies on community search do not consider the influence of a community. In this paper, we introduce a novel community model called k-influential community based on the concept of k-core, which can capture the influence of a community. Based on the new community model, we propose a linear-time online search algorithm to find the top-r k-influential communities in a network. To further speed up the influential community search algorithm, we devise a linear-space index structure which supports efficient search of the top-r k-influential communities in optimal time. We also propose an efficient algorithm to maintain the index when the network is frequently updated. We conduct extensive experiments on 7 real-world large networks, and the results demonstrate the efficiency and effectiveness of the proposed methods.

Link prediction: the power of maximal entropy random walk

Link prediction is a fundamental problem in social network analysis. The key technique in unsupervised link prediction is to find an appropriate similarity measure between nodes of a network. A class of wildly used similarity measures are based on random walk on graph. The traditional random walk (TRW) considers the link structures by treating all nodes in a network equivalently, and ignores the centrality of nodes of a network. However, in many real networks, nodes of a network not only prefer to link to the similar node, but also prefer to link to the central nodes of the network. To address this issue, we use maximal entropy random walk (MERW) for link prediction, which incorporates the centrality of nodes of the network. First, we study certain important properties of MERW on graph

Top-K structural diversity search in large networks

G

On random walk based graph sampling

by constructing an eigen-weighted graph G. We show that the transition matrix and stationary distribution of MERW on G are identical to the ones of TRW on G. Based on G, we further give the maximal entropy graph Laplacians, and show how to fast compute the hitting time and commute time of MERW. Second, we propose four new graph kernels and two similarity measures based on MERW for link prediction. Finally, to exhibit the power of MERW in link prediction, we compare 27 various link prediction methods over 3 synthetic and 8 real networks. The results show that our newly proposed MERW based methods outperform the state-of-the-art method on most datasets.

Measuring the impact of MVC attack in large complex networks

Social contagion depicts a process of information (e.g., fads, opinions, news) diffusion in the online social networks. A recent study reports that in a social contagion process the probability of contagion is tightly controlled by the number of connected components in an individuals neighborhood. Such a number is termed structural diversity of an individual and it is shown to be a key predictor in the social contagion process. Based on this, a fundamental issue in a social network is to find top-k users with the highest structural diversities. In this paper, we, for the first time, study the top-k structural diversity search problem in a large network. Specifically, we develop an effective upper bound of structural diversity for pruning the search space. The upper bound can be incrementally refined in the search process. Based on such upper bound, we propose an efficient framework for top-k structural diversity search. To further speed up the structural diversity evaluation in the search process, several carefully devised heuristic search strategies are proposed. Extensive experimental studies are conducted in 13 real-world large networks, and the results demonstrate the efficiency and effectiveness of the proposed methods.

Triangle minimization in large networks

Random walk based graph sampling has been recognized as a fundamental technique to collect uniform node samples from a large graph. In this paper, we first present a comprehensive analysis of the drawbacks of three widely-used random walk based graph sampling algorithms, called re-weighted random walk (RW) algorithm, Metropolis-Hastings random walk (MH) algorithm and maximum-degree random walk (MD) algorithm. Then, to address the limitations of these algorithms, we propose two general random walk based algorithms, named rejection-controlled Metropolis-Hastings (RCMH) algorithm and generalized maximum-degree random walk (GMD) algorithm. We show that RCMH balances the tradeoff between the limitations of RW and MH, and GMD balances the tradeoff between the drawbacks of RW and MD. To further improve the performance of our algorithms, we integrate the so-called delayed acceptance technique and the non-backtracking random walk technique into RCMH and GMD respectively. We conduct extensive experiments over four real-world datasets, and the results demonstrate the effectiveness of the proposed algorithms.

A topic-biased user reputation model in rating systems

Measuring the impact of network attack is an important issue in network science. In this paper, we study the impact of maximal vertex coverage (MVC) attack in large complex networks, where the attacker aims at deleting as many edges of the network as possible by attacking a small fraction of nodes. First, we present two metrics to measure the impact of MVC attack. To compute these metrics, we propose an efficient randomized greedy algorithm with near-optimal performance guarantee. Second, we generalize the MVC attack into an uncertain setting, in which a node is deleted by the attacker with a prior probability. We refer to the MVC attack under such uncertain environment as the probabilistic MVC attack. Based on the probabilistic MVC attack, we propose two adaptive metrics, and then present an adaptive greedy algorithm for calculating such metrics accurately and efficiently. Finally, we conduct extensive experiments on 20 real datasets. The results show that P2P and co-authorship networks are extremely robust under the MVC attack while both the online social networks and the Email communication networks exhibit vulnerability under the MVC attack. In addition, the results demonstrate the efficiency and effectiveness of the proposed algorithms for computing the proposed metrics.

Scalable Diversified Ranking on Large Graphs

The number of triangles is a fundamental metric for analyzing the structure and function of a network. In this paper, for the first time, we investigate the triangle minimization problem in a network under edge (node) attack, where the attacker aims to minimize the number of triangles in the network by removing