Mining Stable Communities in Temporal Networks by Density-Based Clustering

Many real-world networks evolve over time, that is, new contacts appear and old contacts may disappear. They can be modeled as temporal graphs where interactions between vertices (which represent people in the case of social networks) are represented by time-stamped edges. One of the most fundamental problems in (social) network analysis is community detection, and one of the most basic primitives to model a community is a clique. Addressing the problem of finding communities in temporal networks, Viard et al. [TCS 2016] introduced $Δ$-cliques as a natural temporal version of cliques. Himmel et al. [SNAM 2017] showed how to adapt the well-known Bron-Kerbosch algorithm to enumerate $Δ$-cliques. We continue this work and improve and extend the algorithm of Himmel et al. to enumerate temporal $k$-plexes (notably, cliques are the special case $k=1$). We define a $Δ$-$k$-plex as a set of vertices and a time interval, where during this time interval each vertex has in each consecutive $Δ+ 1$ time steps at least one edge to all but at most $k-1$ vertices in the chosen set of vertices. We develop a recursive algorithm for enumerating all maximal $Δ$-$k$-plexs and perform experiments on real-world social networks that demonstrate the practical feasibility of our approach. In particular, for the special case of $Δ$-1-plexes (that is, $Δ$-cliques), we observe that our algorithm is on average significantly faster than the previous algorithms by Himmel et al. [SNAM 2017] and Viard et al. [IPL 2018] for enumerating $Δ$-cliques.

Community structure is a fundamental feature for many networks. The problem of discovering communities in those networks thus has been attracting a lot of research. However, due to the rapid increase of networks’ scale and the availability of real communities in many networks, the task of detecting communities in large real networks remains a challenging problem. In this paper, we study the structure of various large real networks and their ground-truth community structures and observe an interesting phenomenon: the difference of degrees (abbreviated as dod) of connected nodes follows a heavy-tailed distribution with an approximate power-law tail for large dod, in both original network and community structure but to different extents. With the aim to explore the effect of this observation on identifying communities in real large networks, we propose a weighting strategy and further embed it into two prominent community detection algorithms. Comparisons against the state of the arts demonstrate a very promising performance of the proposed weighting strategy.

Community detection is an effective approach to unveil relationships among individuals in online social networks. In the literature, quite a few algorithms have been proposed to conduct community detection by exploiting the topology of social networks and the attributes of social actors. In practice, community detection is usually conducted by third parties, such as advertisement companies and hospitals, with access to social networks for different purposes, which can easily lead to a privacy breach. In this paper, we investigate community detection in social networks aiming to protect the privacy of both the network topology and the users' attributes. We show that with additional prior knowledge, community detection can be performed by querying the information of only a fraction of instead of the entire population. In particular, we first propose a new scheme called differentially private community detection (DPCD). DPCD detects communities in social networks via a probabilistic generative model, which can be decomposed into subproblems solved by individual users. The private social relationships and attributes of each user are protected by objective perturbation with differential privacy guarantees. Then, we propose a parsimonious node affiliation recovery (NAR) algorithm, which is also differentially private, to unveil the community affiliation information of the whole population based on that of the limited number of queried individuals by solving a sparse optimization problem. Through both theoretical analysis and experimental validation using synthetic and real-world social networks, we demonstrate that the proposed DPCD scheme detects social communities under the modest privacy budget. In addition, we show the effectiveness of NAR to perform community detection by querying a limited number of individuals in social networks.

Searching for local communities is an important research challenge that allows for personalized community discovery and supports advanced data analysis in various complex networks, such as the World Wide Web, social networks, and brain networks. The evolution of these networks over time has motivated several recent studies to identify local communities in temporal networks. Given any query nodes, Community Search aims to find a densely connected subgraph containing query nodes. However, existing community search approaches in temporal networks have two main limitations: (1) they adopt pre-defined subgraph patterns to model communities, which cannot find communities that do not conform to these patterns in real-world networks, and (2) they only use the aggregation of disjoint structural information to measure quality, missing the dynamic of connections and temporal properties. In this paper, we propose a query-driven Temporal Graph Convolutional Network (CS-TGN) that can capture flexible community structures by learning from the ground-truth communities in a data-driven manner. CS-TGN first combines the local query-dependent structure and the global graph embedding in each snapshot of the network and then uses a GRU cell with contextual attention to learn the dynamics of interactions and update node embeddings over time. We demonstrate how this model can be used for interactive community search in an online setting, allowing users to evaluate the found communities and provide feedback. Experiments on real-world temporal graphs with ground-truth communities validate the superior quality of the solutions obtained and the efficiency of our model in both temporal and interactive static settings.

Detecting communities in complex networks and particularly in social networks have been gaining traction in recent years. Not much work has been undertaken in the area of Community Detection for patient-centric social networks. In this work, we have tried to detect significant communities in a patient-centric social network by computing similarity among the unstructured physician notes which are in the form of long texts. Experiments have been conducted using the MIMIC III dataset, which is a large open database containing de-identified health-related patient data. Three modularity based community detection algorithms, viz., FastGreedy, Walktrap, and Louvain have been applied to identify the potential communities in the network. Further, the significance of such communities has been tested using the Wilcoxon rank-total test. It is found that Louvain algorithm fared better in terms of modularity and significance compared to the other two algorithms.

Many famous online social networks, e.g., Facebook and Twitter, have achieved great success in the last several years. Users in these online social networks can establish various connections via both social links and shared attribute information. Discovering groups of users who are strongly connected internally is defined as the community detection problem. Community detection problem is very important for online social networks and has extensive applications in various social services. Meanwhile, besides these popular social networks, a large number of new social networks offering specific services also spring up in recent years. Community detection can be even more important for new networks as high quality community detection results enable new networks to provide better services, which can help attract more users effectively. In this paper, we will study the community detection problem for new networks, which is formally defined as the “New Network Community Detection” problem. New network community detection problem is very challenging to solve for the reason that information in new networks can be too sparse to calculate effective similarity scores among users, which is crucial in community detection. However, we notice that, nowadays, users usually join multiple social networks simultaneously and those who are involved in a new network may have been using other well-developed social networks for a long time. With full considerations of network difference issues, we propose to propagate useful information from other well-established networks to the new network with efficient information propagation models to overcome the shortage of information problem. An effective and efficient method, Cat (Cold stArT community detector), is proposed in this paper to detect communities for new networks using information from multiple heterogeneous social networks simultaneously. Extensive experiments conducted on real-world heterogeneous online social networks demonstrate that Cat can address the new network community detection problem effectively.

A spreading activation-based label propagation algorithm for overlapping community detection in dynamic social networks

Temporal dynamics of social interaction networks as well as the analysis of communities are key aspects to gain a better understanding of the involved processes, important influence factors, their effects, and their structural implications. In this article, we analyze temporal dynamics of contacts and the evolution of communities in networks of face-to-face proximity. As our application context, we consider four scientific conferences. On a structural level, we focus on static and dynamic properties of the contact graphs. Also, we analyze the resulting community structure using state-of-the-art automatic community detection algorithms. Specifically, we analyze the evolution of contacts and communities over time to consider the stability of the respective communities. Furthermore, we assess different factors which have an influence on the quality of community prediction. Overall, we provide first important insights into the evolution of contacts and communities in face-to-face contact networks.

Community detection has arisen as one of the most relevant topics in the field of graph data mining due to its applications in many fields such as biology, social networks, or network traffic analysis. Although the existing metrics used to quantify the quality of a community work well in general, under some circumstances, they fail at correctly capturing such notion. The main reason is that these metrics consider the internal community edges as a set, but ignore how these actually connect the vertices of the community. We propose the Weighted Community Clustering ( WCC ), which is a new community metric that takes the triangle instead of the edge as the minimal structural motif indicating the presence of a strong relation in a graph. We theoretically analyse WCC in depth and formally prove, by means of a set of properties, that the maximization of WCC guarantees communities with cohesion and structure. In addition, we propose Scalable Community Detection (SCD) , a community detection algorithm based on WCC , which is designed to be fast and scalable on SMP machines, showing experimentally that WCC correctly captures the concept of community in social networks using real datasets. Finally, using ground-truth data, we show that SCD provides better quality than the best disjoint community detection algorithms of the state of the art while performing faster.

A cascade information diffusion based label propagation algorithm for community detection in dynamic social networks

Parallel and distributed paradigms for community detection in social networks: A methodological review

Complex networks arise in various fields, such as biology, sociology and communication, to model interactions among entities. Entities in many real-world systems exhibit different types of interactions, which requires modeling these type of systems properly. Multiplex networks are used to model these systems, as they can reflect the nodes’ pair-wise interactions as multiple distinct types of links across layers. Community detection is a widely studied application in network analysis as it provides insights into the structure and organization of the network. Even though multiple algorithms have been developed in the community detection field, many of them have a limited performance in the presence of noise. In this article, we develop a novel algorithm that combines tensor low-rank representation, spectral clustering and distance regularization to improve the accuracy in discovering communities in multiplex networks. The low-rank representation leads to reducing the noise and errors existing in the network and the optimization of an accurate consensus set of eigenvectors that reveals the communities in the network. Moreover, the proposed approach balances the agreement between the eigenvectors of each layer, i.e., individual subspaces, and the consensus set of eigenvectors, i.e., common subspaces, by minimizing the projection distance between them. The common and individual subspaces are computed efficiently through Tucker decomposition and modified spectral clustering, respectively. Finally, multiple experiments are conducted on real and simulated networks to evaluate the proposed approach and compare it to state-of-the-art algorithms. The proposed approach shows its robustness and efficiency in discovering the communities in multiplex networks.

Detecting community structure by belonging intensity analysis of intermediate nodes

Multiplex graphs have been recently proposed as a model to represent high-level complexity in real-world networks such as heterogeneous social networks where actors could be characterized by heterogeneous properties and could be linked with different types of social interactions. This has brought new challenges in community detection, which aims to identify pertinent groups of nodes in a complex graph. In this context, great efforts have been made to tackle the problem of community detection in multiplex graphs. However, most of the proposed methods until recently deal with static multiplex graph and ignore the temporal dimension, which is a key characteristic of real networks. Even more, the few methods that consider temporal graphs, they just propose to follow communities over time and none of them use the temporal aspect directly to detect stable communities, which are often more meaningful in reality. Thus, this paper proposes a new two-step method to detect stable communities in temporal multiplex graphs. The first step aims to find the best static graph partition at each instant by applying a new hybrid community detection algorithm, which considers both relations heterogeneities and nodes similarities. Then, the second step considers the temporal dimension in order to find final stable communities. Finally, experiments on synthetic graphs and a real social network show that this method is competitive and it is able to extract high-quality communities.

Social networks are ubiquitous in our daily life. Due to the rapid development of information and electronic technology, social networks are becoming more and more complex in terms of sizes and contents. It is of paramount significance to analyse the structures of social networks in order to unveil the myth beneath complex social networks. Network community detection is recognised as a fundamental tool towards social networks analytics. As a consequence, numerical community detection methods are proposed in the literature. For a real-world social network, an individual may possess multiple memberships, while the existing community detection methods are mainly designed for non-overlapping situations. With regard to this, this paper proposes a hybrid metaheuristic method to detect overlapping communities in social networks. In the proposed method, the overlapping community detection problem is formulated as an optimisation problem and a novel bat optimisation algorithm is designed to solve the established optimisation model. To enhance the searchability of the proposed algorithm, a local search operator based on tabu search is introduced. To validate the effectiveness of the proposed algorithm, experiments on benchmark and real-world social networks are carried out. The experiments indicate that the proposed algorithm is promising for overlapping community detection.