Real-world networks often involve both keywords and locations, along with travel time variations between locations due to traffic conditions. However, most existing cohesive subgraph-based community search studies utilize a single attribute, either keywords or locations, to identify communities. They do not simultaneously consider both keywords and locations, which results in low semantic or spatial cohesiveness of the detected communities, and they fail to account for variations in travel time. Additionally, these studies traverse the entire network to build efficient indexes, but the detected community only involves nodes around the query node, leading to the traversal of nodes that are not relevant to the community. Therefore, we propose the problem of discovering semantic-spatial aware k-core, which refers to a k-core with high semantic and time-dependent spatial cohesiveness containing the query node. To address this problem, we propose an exact and a greedy algorithm, both of which gradually expand outward from the query node. They are local methods that only access the local part of the attributed network near the query node rather than the entire network. Moreover, we design a method to calculate the semantic similarity between two keywords using large language models. This method alleviates the disadvantages of keyword-matching methods used in existing community search studies, such as mismatches caused by differently expressed synonyms and the presence of irrelevant words. Experimental results show that the greedy algorithm outperforms baselines in terms of structural, semantic, and time-dependent spatial cohesiveness.
Semi-supervised local community detection aims to leverage known communities to detect the community containing a given node. Although existing semi-supervised local community detection studies yield promising results, they suffer from time-consuming issues, highlighting the need for more efficient algorithms. Therefore, we apply the "pre-train, prompt" paradigm to semi-supervised local community detection and propose the Pre-trained Prompt-driven Semi-supervised Local community detection method (PPSL). PPSL consists of three main components: node encoding, sample generation, and prompt-driven fine-tuning. Specifically, the node encoding component employs graph neural networks to learn the representations of nodes and communities. Based on representations of nodes and communities, the sample generation component selects known communities that are structurally similar to the local structure of the given node as training samples. Finally, the prompt-driven fine-tuning component leverages these training samples as prompts to guide the final community prediction. Experimental results on five real-world datasets demonstrate that PPSL outperforms baselines in both community quality and efficiency.
Recently, numerous community search methods for large graphs have been proposed, at the core of which is defining and measuring cohesion. This paper experimentally evaluates the effectiveness of these community search algorithms w.r.t. cohesiveness in the context of online social networks. Social communities are formed and developed under the influence of group cohesion theory, which has been extensively studied in social psychology. However, current generic methods typically measure cohesiveness using structural or attribute-based approaches and overlook domain-specific concepts such as group cohesion. We introduce five novel psychology-informed cohesiveness measures, based on the concept of group cohesion from social psychology, and propose a novel framework called CHASE for evaluating eight representative community search algorithms w.r.t. these measures on online social networks. Our analysis reveals that there is no clear correlation between structural and psychological cohesiveness, and no algorithm effectively identifies psychologically cohesive communities in online social networks. This study provides new insights that could guide the development of future community search methods.
Aggregated relative search frequencies offer a unique composite signal reflecting people's habits, concerns, interests, intents, and general information needs, which are not found in other readily available datasets. Temporal search trends have been successfully used in time series modeling across a variety of domains such as infectious diseases, unemployment rates, and retail sales. However, most existing applications require curating specialized datasets of individual keywords, queries, or query clusters, and the search data need to be temporally aligned with the outcome variable of interest. We propose a novel approach for generating an aggregated and anonymized representation of search interest as foundation features at the community level for geospatial modeling. We benchmark these features using spatial datasets across multiple domains. In zip codes with a population greater than 3000 that cover over 95% of the contiguous US population, our models for predicting missing values in a 20% set of holdout counties achieve an average $R^2$ score of 0.74 across 21 health variables, and 0.80 across 6 demographic and environmental variables. Our results demonstrate that these search features can be used for spatial predictions without strict temporal alignment, and that the resulting models outperform spatial interpolation and state of the art methods using satellite imagery features.
Community Search (CS) aims to identify densely interconnected subgraphs corresponding to query vertices within a graph. However, existing heterogeneous graph-based community search methods need help identifying cross-group communities and suffer from efficiency issues, making them unsuitable for large graphs. This paper presents a fast community search model based on the Butterfly-Core Community (BCC) structure for heterogeneous graphs. The Random Walk with Restart (RWR) algorithm and butterfly degree comprehensively evaluate the importance of vertices within communities, allowing leader vertices to be rapidly updated to maintain cross-group cohesion. Moreover, we devised a more efficient method for updating vertex distances, which minimizes vertex visits and enhances operational efficiency. Extensive experiments on several real-world temporal graphs demonstrate the effectiveness and efficiency of this solution.
Community search is a derivative of community detection that enables online and personalized discovery of communities and has found extensive applications in massive real-world networks. Recently, there needs to be more focus on the community search issue within directed graphs, even though substantial research has been carried out on undirected graphs. The recently proposed D-truss model has achieved good results in the quality of retrieved communities. However, existing D-truss-based work cannot perform efficient community searches on large graphs because it consumes too many computing resources to retrieve the maximal D-truss. To overcome this issue, we introduce an innovative merge relation known as D-truss-connected to capture the inherent density and cohesiveness of edges within D-truss. This relation allows us to partition all the edges in the original graph into a series of D-truss-connected classes. Then, we construct a concise and compact index, ConDTruss, based on D-truss-connected. Using ConDTruss, the efficiency of maximum D-truss retrieval will be greatly improved, making it a theoretically optimal approach. Experimental evaluations conducted on large directed graph certificate the effectiveness of our proposed method.
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.
Community Search (CS) is one of the fundamental tasks in network science and has attracted much attention due to its ability to discover personalized communities with a wide range of applications. Given any query nodes, CS seeks to find a densely connected subgraph containing query nodes. Most existing approaches usually study networks with a single type of proximity between nodes, which defines a single view of a network. However, in many applications such as biological, social, and transportation networks, interactions between objects span multiple aspects, yielding networks with multiple views, called multiplex networks. Existing CS approaches in multiplex networks adopt pre-defined subgraph patterns to model the communities, which cannot find communities that do not have such pre-defined patterns in real-world networks. In this paper, we propose a query-driven graph convolutional network in multiplex networks, CS-MLGCN, that can capture flexible community structures by learning from the ground-truth communities in a data-driven fashion. CS-MLGCN first combines the local query-dependent structure and global graph embedding in each type of proximity and then uses an attention mechanism to incorporate information on different types of relations. Experiments on real-world graphs with ground-truth communities validate the quality of the solutions we obtain and the efficiency of our model.
A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in studying numerous subgraph problems, on top of the ordinary graph problems. Many algorithms are proposed in studying subgraph problems, where one common approach is by extracting the patterns and structures of a given graph. Due to the complex structures of certain types of graphs and to improve overall performances of the existing frameworks, machine learning techniques have recently been employed in dealing with various subgraph problems. In this article, we present a comprehensive review on five well known subgraph problems that have been tackled by using machine learning methods. They are subgraph isomorphism (both counting and matching), maximum common subgraph, community detection and community search problems. We provide an outline of each proposed method, and examine its designs and performances. We also explore non-learning-based algorithms for each problem and a brief discussion is given. We then suggest some promising research directions in this area, hoping that relevant subgraph problems can be tackled by using a similar strategy. Since there is a huge growth in employing machine learning techniques in recent years, we believe that this survey will serve as a good reference point to relevant research communities.
Given one or more query vertices, Community Search (CS) aims to find densely intra-connected and loosely inter-connected structures containing query vertices. Attributed Community Search (ACS), a related problem, is more challenging since it finds communities with both cohesive structures and homogeneous vertex attributes. However, most methods for the CS task rely on inflexible pre-defined structures and studies for ACS treat each attribute independently. Moreover, the most popular ACS strategies decompose ACS into two separate sub-problems, i.e., the CS task and subsequent attribute filtering task. However, in real-world graphs, the community structure and the vertex attributes are closely correlated to each other. This correlation is vital for the ACS problem. In this paper, we propose Graph Neural Network models for both CS and ACS problems, i.e., Query Driven-GNN and Attributed Query Driven-GNN. In QD-GNN, we combine the local query-dependent structure and global graph embedding. In order to extend QD-GNN to handle attributes, we model vertex attributes as a bipartite graph and capture the relation between attributes by constructing GNNs on this bipartite graph. With a Feature Fusion operator, AQD-GNN processes the structure and attribute simultaneously and predicts communities according to each attributed query. Experiments on real-world graphs with ground-truth communities demonstrate that the proposed models outperform existing CS and ACS algorithms in terms of both efficiency and effectiveness. More recently, an interactive setting for CS is proposed that allows users to adjust the predicted communities. We further verify our approaches under the interactive setting and extend to the attributed context. Our method achieves 2.37% and 6.29% improvements in F1-score than the state-of-the-art model without attributes and with attributes respectively.
We introduce a novel keyword-aware influential community query KICQ that finds the most influential communities from an attributed graph, where an influential community is defined as a closely connected group of vertices having some dominance over other groups of vertices with the expertise (a set of keywords) matching with the query terms (words or phrases). We first design the KICQ that facilitates users to issue an influential CS query intuitively by using a set of query terms, and predicates (AND or OR). In this context, we propose a novel word-embedding based similarity model that enables semantic community search, which substantially alleviates the limitations of exact keyword based community search. Next, we propose a new influence measure for a community that considers both the cohesiveness and influence of the community and eliminates the need for specifying values of internal parameters of a network. Finally, we propose two efficient algorithms for searching influential communities in large attributed graphs. We present detailed experiments and a case study to demonstrate the effectiveness and efficiency of the proposed approaches.