Graphlets are small, connected, and non-isomorphic induced subgraphs that describe the topological structure of a graph. Counting graphlets is a fundamental task in graph mining and social network analysis. It has numerous applications in many fields, including dense subgraph discovery, anomaly detection, etc. Most existing work assumes a static graph. However, graphs are dynamic in the real world, which can be described as graph streams. Counting graphlets in graph streams is a challenge due to the streaming nature of the input. While there have been several studies on counting graphlets in graph streams, these works are limited to simple graphlets like triangles and butterflies. In this paper, we propose SGES algorithm to estimate more complex graphlets in graph streams. In SGES, we first propose an unbiased sampling strategy to maintain fixed-size sampled edges, which in turn allows us to unbiasedly estimate the number of subgraphs and then count graphlets based on the combinational relationship between the number of subgraphs and the number of graphlets. Extensive experiments over large real-world graph streams prove that our algorithm can obtain accurate estimation values of graphlet counts with high throughput.

A frequency bursting pattern (FBP) in temporal graphs represents some interaction behavior that accumulates its frequency at the fastest rate. Mining FBPs is essential to early warning of emergencies. However, existing studies on frequency-based pattern mining in graphs do not consider the temporal information and bursting features of a subgraph pattern. As a result, they may not provide effective and efficient mining algorithms for FBP discovery. In this paper, we study the problem of discovering top-k FBPs in temporal graphs. We present a novel model, referred to as maximal (m, θ)-bursting pattern, to describe FBPs in a temporal graph, which is a subgraph with a size larger than m that accumulates its frequency at the fastest rate during a time interval of length no less than θ. A naive solution for top-k FBPs discovery is to use the best-first search algorithm, where the burstiness threshold changes as more patterns are mined. However, this method will result in huge search space since we need to check every possible time interval for a candidate pattern in the temporal graph. To tackle this problem, we devise an online top-k framework in which k candidate results are maintained from the initial timestamp to the end in the temporal graph. Under the new framework, we further conceive two optimization strategies by exploiting incremental subgraph matching and Evolutionary Game Theory to boost the performance. Extensive experiment results on five real temporal graphs show that our algorithm has higher efficiency, effectiveness and scalability.

Abstract With the rapid development of information technologies, multi-source heterogeneous data has become an open problem, and the data is usually modeled as graphs since the graph structure is able to encode complex relationships among entities. However, in practical applications, such as network security analysis and public opinion analysis over social networks, the structure and the content of graph data are constantly evolving. Therefore, the ability to continuously monitor and detect interesting patterns on massive and dynamic graphs in real-time is crucial for many applications. Recently, a large group of excellent research works has also emerged. Nevertheless, these studies focus on different updates of graphs and apply different subgraph matching algorithms; thus, it is desirable to review these works comprehensively and give a thorough overview. In this paper, we systematically investigate the existing continuous subgraph matching techniques from the aspects of key techniques, representative algorithms, and performance evaluation. Furthermore, the typical applications and challenges of continuous subgraph matching over dynamic graphs, as well as the future development trends, are summarized and prospected.

RDF stream processing (RSP) has become a vibrant area of research in the Semantic Web community, which guarantees interoperability and opens up important applications. There have been efforts to extend RDF data and SPARQL query for representing streaming information and continuous querying functionalities. However, existing solutions will incur significant low throughput due to the recomputation of the results from scratch as the window slides. In this paper, we propose a novel graph-based framework, referred as IncTreeRDF, towards continuous SPARQL query evaluation over RDF data streams. Under the framework, the RDF data streams are modeled as streaming graphs; the SPARQL queries are translated into graph patterns and evaluated via continuous sub-graph pattern-matching over streaming RDF graphs. IncTreeRDF employs a query-centric auxiliary data structure called TStore to store some intermediate results, which supports fast incremental maintenance. Based on TStore, we can not only avoid re-computing matches of the query but also prune invalid updates. Besides, we define matching-free update, in which subgraph matching calculation can be avoided under this scenario. Extensive experimental results show that IncTreeRDF significantly outperforms existing competitors.

\emphSeasonal periodicity is a frequent phenomenon for social interactions in temporal networks. A key property of this behavior is that it exhibits periodicity for multiple particular periods in temporal networks. Mining such seasonal-periodic patterns is significant since it can indicate interesting relationships between the individuals involved in the interactions. Unfortunately, most previous studies for periodic pattern mining ignore the seasonal feature. This motivates us to explore mining seasonal-periodic subgraphs, and the investigation presents a novel model, called maximal σ-periodic $ømega$-seasonal k-subgraph. It represents a subgraph with size larger than k and that appears at least σ times periodically in at least $ømega$ particular periods on the temporal graph. Since seasonal-periodic patterns do not satisfy the anti-monotonic property, we propose a weak version of support measure with an anti-monotonic property to reduce the search space efficiently. Then, we present an effective mining algorithm to seek all maximal σ-periodic $ømega$-seasonal k-subgraphs. Experimental results on real-life datasets show the effectiveness and efficiency of our approach.

An evolving pattern graph is defined by an initial pattern graph and a graph update stream consisting of edge insertions and deletions. Identifying and monitoring evolving graph patterns in the data graph is important in various application domains such as Cyberthreats surveillance. This motivates us to explore matching patterns with evolvement, and the investigation presents a novel algorithm \incepg for continuously matching of evolving patterns. Specially, we propose a concise representation \Index of partial matching solutions, and its execution model allows fast incremental maintenance. We also conceive an effective model for estimating step-wise cost of pattern evaluation to drive the matching process. Extensive experiments verify the superiority of \incepg.