Graph data is found in numerous domains such as for the analysis of social networks, sensor networks, bioinformatics, industrial systems, and chemistry. Analyzing graphs to identify useful and interesting patterns is an important research area. It helps understanding graphs, and hence support decision making. Since two decades, many graph mining algorithms have been proposed to identify patterns such as frequent subgraphs, paths, cliques, and trees. But most of them assume that graphs are static. This simplifying assumption makes it easy to design algorithms but discard information about how graphs evolve. This article provides a detailed survey of techniques for mining interesting patterns in dynamic graphs, which can serve both as an introduction and as a guide to recent advances and opportunities in this research area. The main tasks related to mining patterns in dynamic graphs are reviewed such as discovering frequent subgraphs, evolution rules, motifs, subgraph sequences, recurrent and triggering patterns, and trend sequences. In addition, an overview of strategies and approaches to solve dynamic graph mining problems is presented, and their advantages and limitations are highlighted. Various extensions are also discussed such as to discover patterns in data streams and big data. Finally, the article mentions several research opportunities.
A dynamic attributed graph is a graph that changes over time and where each vertex is described using multiple continuous attributes. Such graphs are found in numerous domains, e.g., social network analysis. Several studies have been done on discovering patterns in dynamic attributed graphs to reveal how attribute(s) change over time. However, many algorithms restrict all attribute values in a pattern to follow the same trend (e.g. increase) and the set of vertices in a pattern to be fixed, while others consider that a single vertex may influence its neighbors. As a result, these algorithms are unable to find complex patterns that show the influence of multiple vertices on many other vertices in terms of several attributes and different trends. This paper addresses this issue by proposing to discover a novel type of patterns called attribute evolution rules (AER). These rules indicate how changes of attribute values of multiple vertices may influence those of others with a high confidence. An efficient algorithm named AER-Miner is proposed to find these rules. Experiments on real data show AER-Miner is efficient and that AERs can provide interesting insights about dynamic attributed graphs.
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