Simplifying social networks via triangle-based cohesive subgraphs

With the proliferation of social network services (e.g., Facebook, Twitter, and Instagram), identifying cohesive subgraphs in networks is a key and fundamental problem to understand users' activity. Recently this problem has received extensive research attention. Identifying cohesive subgraph structures in networks has many applications such as recommendation, detecting fraudsters, event organization, and graph analysis. In this thesis, we study three important problems of finding cohesive subgraphs. Our studies include finding a query-based cohesive subgraph search in social networks and location-based social networks, and detecting all cohesive subgraphs in attributed bipartite networks. In our study of Density Modularity based Community Search (DMCS), we propose the modularity-based community search problem in networks. Modularity is a widely used measure of the structure of networks which checks the strength of partition of a network into communities. Most of the existing community search models only focus on the internal cohesiveness of a community. However, a high-quality community often has high modularity, which implies dense connections inside communities and sparse connections to the nodes outside the community. Hence, we conduct a pioneer study on searching for a community with high modularity. We point out that while modularity has been used in community detection (unrelated to query nodes), its application in community search (related to query nodes) brings in different challenges named free-rider effect and resolution limit problems. Both problems indicate that intrinsically optimizing the modularity can fail to find a small-sized community as a result for the community search problem. We mitigate these problems by designing a new graph modularity function named Density Modularity. To the best of our knowledge, this is the first work on the community search problem by using the graph modularity. The community search based on the density modularity, termed as DMCS, is to find a community in a social network that contains all the query nodes and has high density modularity. We prove that the DMCS problem is NP-hard, and thus there is no exact algorithm that is scalable to large graphs. To efficiently address DMCS, we present new algorithms that run in log-linear time to the graph size. We conduct extensive experimental studies in real-world and synthetic networks, which offer insights into the efficiency and effectiveness of our approximate algorithms. In our study of GeoSocial Community Search(GCS) problem, we propose the community search problem in location-based social networks. Specifically, we aim at finding a social community and a location cluster that are densely connected in a location-based social network. GCS can be useful for finding marketing targets and user/location recommendations. To the best of our knowledge, this is the first work to find a social community and a location cluster that are densely connected from location-based social networks. We prove that the GCS problem is NP-hard and is not in APX, unless P = NP. To solve GCS problem, we propose three effective and efficient algorithms: Core-based Basic Algorithm, Top-down Greedy Removing Algorithm, and Bottom-up Greedy Expansion Algorithms. Finally, we report extensive experimental studies that offer insights into the efficiency and effectiveness of the proposed solutions. In our study of Attributed Bipartite Co-clustering (ABC), we propose the co-clustering problem in attributed bipartite networks. Co-clustering in bipartite networks is a fundamental and important problem. Specifically, we unify two main concepts: (i) bipartite modularity optimization, and (ii) attribute cohesiveness. To the best of our knowledge, this is the first work to find a set of co-clusters while considering the attribute cohesiveness. We prove that ABC problem is NP-hard and propose three effective and efficient algorithms: (1) Top-Down Algorithm; (2) Bottom-Up Algorithm; and (3) Group-based Matching Algorithm. Finally, extensive experimental results on real-world attributed bipartite networks demonstrate the efficiency and effectiveness of our algorithms.

In recent years, cohesive subgraph mining in bipartite graphs becomes a popular research topic. An important cohesive subgraph model k-bitruss is the maximal cohesive subgraph where each edge is contained in at least k butterflies (i.e., (2, 2)-bicliques). In this paper, we study the bitruss decomposition problem which aims to find all the k-bitrusses for $$k \ge 0$$ . The existing algorithms follow a bottom-up strategy which peels the edges with the lowest butterfly support iteratively. In this peeling process, these algorithms are time-consuming to enumerate all the supporting butterflies for each edge. To solve this issue, we propose a novel online index, the $$\mathsf {BE}$$ - $$\mathsf {Index}$$ which compresses butterflies into k-blooms (i.e., (2, k)-bicliques). Based on the $$\mathsf {BE}$$ - $$\mathsf {Index}$$ , the new bitruss decomposition algorithm $$\mathsf {BiT}$$ - $$\mathsf {BU}$$ is proposed, along with two batch-based optimizations, to accomplish the butterfly enumeration of the peeling process efficiently. Furthermore, the $$\mathsf {BiT}$$ - $$\mathsf {PC}$$ algorithm is designed which is more efficient against handling the edges with high butterfly supports. Besides, we explore shared-memory parallel solutions to handle large graphs in a more efficient way. In the parallel algorithms, we propose effective techniques to reduce conflicts among threads. We theoretically show that our new algorithms significantly reduce the time complexities of the existing algorithms. In addition, extensive empirical evaluations are conducted on real-world datasets. The experimental results further validate the effectiveness of the bitruss model and demonstrate that our proposed solutions significantly outperform the state-of-the-art techniques by several orders of magnitude.

Dense core model for cohesive subgraph discovery

Cohesive subgraph mining is a fundamental problem in the field of graph data analysis. Many existing cohesive graph mining algorithms are mainly tailored to deterministic graphs. Real-world graphs, however, are often not deterministic, but uncertain in nature. Applications of such uncertain graphs include protein-protein interactions networks with experimentally inferred links and sensor networks with uncertain connectivity links. In this article, we study the problem of mining cohesive subgraphs from an uncertain graph. Specifically, we introduce a new <inline-formula><tex-math notation="LaTeX">$(\alpha,\gamma)$</tex-math></inline-formula> -quasi-clique model to model the cohesive subgraphs in an uncertain graph, and propose a basic enumeration algorithm to find all maximal <inline-formula><tex-math notation="LaTeX">$(\alpha,\gamma)$</tex-math></inline-formula> -quasi-cliques. We also develop an advanced enumeration algorithm based on several novel pruning rules, including early termination and candidate set reduction. To further improve the efficiency, we propose several optimization techniques. Extensive experiments on five real-world datasets demonstrate that our solutions are almost three times faster than the baseline approach.

Enumerating cohesive subgraphs is a fundamental problem for signed network analysis. In this paper, we propose a novel model, called maximal signed k-clique, which aims to find cohesive subgraphs in signed networks based on clique property and balance theory. Given a signed graph G, a set of nodes C is a maximal signed k-clique if (1) \(|C|\ge k\) and C is a clique without any unbalanced triangle; and (2) C is maximal. We show the problem of enumerating all maximal signed k-cliques is NP-hard. Novel pruning techniques are proposed to significantly filter the searching space. An efficient algorithm, SKC, is developed to handle large networks. Comprehensive experiments on four real-world datasets are conducted to demonstrate the efficiency and effectiveness of the proposed algorithms.

Cohesive subgraph detection is an important graph problem that is widely applied in many application domains, such as social community detection, network visualization, and network topology analysis. Most of existing cohesive subgraph metrics can guarantee good structural properties but may cause the free-rider effect. Here, by free-rider effect, we mean that some irrelevant subgraphs are combined as one subgraph if they only share a small number of vertices and edges. In this paper, we study k-vertex connected component (k-VCC) which can effectively eliminate the free-rider effect but less studied in the literature. A k-VCC is a connected subgraph in which the removal of any k-1 vertices will not disconnect the subgraph. In addition to eliminating the free-rider effect, k-VCC also has other advantages such as bounded diameter, high cohesiveness, bounded graph overlapping, and bounded subgraph number. We propose a polynomial time algorithm to enumerate all k-VCCs of a graph by recursively partitioning the graph into overlapped subgraphs. We find that the key to improving the algorithm is reducing the number of local connectivity testings. Therefore, we propose two effective optimization strategies, namely neighbor sweep and group sweep, to largely reduce the number of local connectivity testings. We conduct extensive performance studies using seven large real datasets to demonstrate the effectiveness of this model as well as the efficiency of our proposed algorithms.

Online force-directed algorithms for visualization of dynamic graphs

Union acceptable profit maximization in social networks

Identifying cohesive subgraphs within networks is a fundamental problem in graph theory, relevant to various domains. The traditional clique problem, which finds fully connected subgraphs, often faces limitations due to its strict connectivity requirements. This paper introduces a novel degree-based relaxation model called Flexi-clique, where the degree constraint is adjusted sub-linearly based on the subgraph size. We establish that the maximum Flexi-clique problem is NP-hard and propose an efficient and effective peeling algorithm to address it. Our extensive experimental evaluation of real-world datasets demonstrates the effectiveness and efficiency of our approach in discovering large, cohesive subgraphs in networks.

The proliferation of rumors on social media has become a major concern due to its ability to create a devastating impact. Manually assessing the veracity of social media messages is a very time-consuming task that can be much helped by machine learning. Most message veracity verification methods only exploit textual contents and metadata. Very few take both textual and visual contents, and more particularly images, into account. Moreover, prior works have used many classical machine learning models to detect rumors. However, although recent studies have proven the effectiveness of ensemble machine learning approaches, such models have seldom been applied. Thus, in this paper, we propose a set of advanced image features that are inspired from the field of image quality assessment, and introduce the Multimodal fusiON framework to assess message veracIty in social neTwORks (MONITOR), which exploits all message features by exploring various machine learning models. Moreover, we demonstrate the effectiveness of ensemble learning algorithms for rumor detection by using five metalearning models. Eventually, we conduct extensive experiments on two real-world datasets. Results show that MONITOR outperforms state-of-the-art machine learning baselines and that ensemble models significantly increase MONITOR’s performance.

Young patients with cancer and a digital social network: the voice beyond the clinic

In recent years, the use of social media networks has increased. With the rise in social network usage, social media businesses have begun to place a greater emphasis on large-scale social network analysis. As a result, several components of the signed network have been studied and analysed. Link prediction is a crucial aspect of this signed network analysis. The majority of previous study focused on forecasting the network&#x2019;s good aspects, such as favourable user connections, but the negative component(i.e., Negative Link) is just as significant as the positive (i.e., positive link). It enhances the performance of several current positive link analysis programmes. As a result, we concentrate on predicting negative ties from a social network that contains both positive and negative interactions in this research. To improve prediction precision, we use social theories such as balancing and status theory. We utilise the XGBoost classifier to determine if a particular missing link is positive or negative. Finally, we use accuracy and F1 measure measures to assess our proposed model.

The problems caused by network dimension disasters and computational complexity have become an important issue to be solved in the field of social network research. The existing methods for network feature learning are mostly based on static and small-scale assumptions, and there is no modified learning for the unique attributes of social networks. Therefore, existing learning methods cannot adapt to the dynamic and large-scale of current social networks. Even super large scale and other features. This paper mainly studies the feature representation learning of large-scale dynamic social network structure. In this paper, the positive and negative damping sampling of network nodes in different classes is carried out, and the dynamic feature learning method for newly added nodes is constructed, which makes the model feasible for the extraction of structural features of large-scale social networks in the process of dynamic change. The obtained node feature representation has better dynamic robustness. By selecting the real datasets of three large-scale dynamic social networks and the experiments of dynamic link prediction in social networks, it is found that DNPS has achieved a large performance improvement over the benchmark model in terms of prediction accuracy and time efficiency. When the α value is around 0.7, the model effect is optimal.

We study the effectiveness of using multiple phases for maximizing the extent of information diffusion through a social network, and present insights while considering various aspects. In particular, we focus on the well-studied independent cascade model with the possibility of adaptively selecting seed nodes in multiple phases based on the observed diffusion in preceding phases, and conduct a detailed simulation study on real-world network datasets. We first present a negative result that more phases do not guarantee a better spread, however the adaptability advantage of using more phases generally leads to a better spread on real-world datasets. We study how diffusing in multiple phases affects the mean and standard deviation of the extent of diffusion, and explain how using multiple phases reduces uncertainty in diffusion. We then study how the number of phases impacts the effectiveness of diffusion, how the diffusion progresses phase-by-phase, and how to optimally split the total seeding budget across phases. Our experiments show a significant gain when we move from single phase to two phases, however, the marginal gain of having an additional phase decreases as we increase the number of phases. Our main conclusion is that, given the number of phases, an optimal way to split the budget across phases is such that the expected number of influenced nodes in each phase is almost the same.

Centrality is an important measure to identify the most important actors in a network. This paper discusses the various Centrality Measures used in Social Network Analysis. These measures are tested on complex real-world social network data sets such as Video Sharing Networks, Social Interaction Network and Co-Authorship Networks to examine their effects on them. We carry out the correlation analysis of these centralities and plot the results to recommend when to use those centrality measures. Additionally, we introduce a new centrality measure - Cohesion Centrality based on the cohesiveness of a graph, develop its sequential algorithm and further devise a parallel algorithm to implement it.