Community detection, which focuses on clustering vertex interactions, plays a significant role in network analysis. However, it also faces numerous challenges like missing data and adversarial attack. How to further improve the performance and robustness of community detection for real-world networks has raised great concerns. In this paper, we explore robust community detection by enhancing network structure, with two generic algorithms presented: one is named robust community detection via genetic algorithm (RobustECDGA), in which the modularity and the number of clusters are combined in a fitness function to find the optimal structure enhancement scheme; the other is called robust community detection via similarity ensemble (RobustECD-SE), integrating multiple information of community structures captured by various vertex similarities, which scales well on large-scale networks. Comprehensive experiments on real-world networks demonstrate, by comparing with two traditional enhancement strategies, that the new methods help six representative community detection algorithms achieve more significant performance improvement. Moreover, experiments on the corresponding adversarial networks indicate that the new methods could also optimize the network structure to a certain extent, achieving stronger robustness against adversarial attack. The source code of this paper is released on https://github.com/jjzhou012/robustECD release.

The spectral radius of the non-backtracking matrix for an undirected graph plays an important role in various dynamic processes running on the graph. For example, its reciprocal provides an excellent approximation of epidemic and edge percolation thresholds. In this paper, we study the problem of minimizing the spectral radius of the non-backtracking matrix of a graph with n nodes and m edges, by deleting k selected edges. We show that the objective function of this combinatorial optimization problem is not submodular, although it is monotone. Since any straightforward approach to solving the optimization problem is computationally infeasible, we present an effective, scalable approximation algorithm with complexity O (n+km). Extensive experiment results for a large set of real-world networks verify the effectiveness and efficiency of our algorithm, and demonstrate that our algorithm outperforms several baseline schemes.

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the underlying network. Although such statistics can be used to describe a network model, or even to design some network algorithms, the role of subgraphs in such applications can be further explored so as to improve the results. In this article, the concept of subgraph network (SGN) is introduced and then applied to network models, with algorithms designed for constructing the 1st-order and 2nd-order SGNs, which can be easily extended to build higher-order ones. Furthermore, these SGNs are used to expand the structural feature space of the underlying network, beneficial for network classification. Numerical experiments demonstrate that the network classification model based on the structural features of the original network together with the 1st-order and 2nd-order SGNs always performs the best as compared to the models based only on one or two of such networks. In other words, the structural features of SGNs can complement that of the original network for better network classification, regardless of the feature extraction method used, such as the handcrafted, network embedding and kernel-based methods.

In social networks, by removing some target-sensitive links, privacy protection might be achieved. However, some hidden links can still be re-observed by link prediction methods on observable networks. In this paper, the conventional link prediction method named Resource Allocation Index (RA) is adopted for privacy attacks. Several defense methods are proposed, including heuristic and evolutionary approaches, to protect targeted links from RA attack. In particular, incremental computation is proposed for accelerating the calculation of fitness in evolutionary approaches. This is the first time to study privacy protection for targeted links against similarity based link prediction attacks. Some links are randomly selected from original network as targeted links for experimentation. The experimental results on nine real-world networks demonstrate the superiority of the evolutionary perturbations, especially EDA, for defending against RA attack. Moreover, experimental results show that the proposed perturbation generated by EDA is transferable and can even defend against other link prediction attacks which are based on high order similarity between pairwise nodes, although it is designed to prevent RA attack.

The issue of opinion sharing and formation has received considerable attention in the academic literature, and a few models have been proposed to study this problem. However, existing models are limited to the interactions among nearest neighbors, ignoring those second, third, and higher-order neighbors, despite the fact that higher-order interactions occur frequently in real social networks. In this paper, we develop a new model for opinion dynamics by incorporating long-range interactions based on higher-order random walks. We prove that the model converges to a fixed opinion vector, which may differ greatly from those models without higher-order interactions. Since direct computation of the equilibrium opinions is computationally expensive, which involves the operations of huge-scale matrix multiplication and inversion, we design a theoretically convergence-guaranteed estimation algorithm that approximates the equilibrium opinion vector nearly linearly in both space and time with respect to the number of edges in the graph. We conduct extensive experiments on various social networks, demonstrating that the new algorithm is both highly efficient and effective.

While the majority of methods for community detection produce disjoint communities of nodes, most real-world networks naturally involve overlapping communities. In this paper, a scalable method for the detection of overlapping communities in large networks is proposed. The method is based on an extension of the notion of normalized cut to cope with overlapping communities. A spectral clustering algorithm is formulated to solve the related cut minimization problem. When available, the algorithm may take into account prior information about the likelihood for each node to belong to several communities. This information can either be extracted from the available metadata or from node centrality measures. We also introduce a hierarchical version of the algorithm to automatically detect the number of communities. In addition, a new benchmark model extending the stochastic blockmodel for graphs with overlapping communities is formulated. Our experiments show that the proposed spectral method outperforms the state-of-the-art algorithms in terms of computational complexity and accuracy on our benchmark graph model and on five real-world networks, including a lexical network and large-scale social networks. The scalability of the proposed algorithm is also demonstrated on large synthetic graphs with millions of nodes and edges.