Graphlet counting is an important problem as it has numerous applications in several fields, including social network analysis, biological network analysis, transaction network analysis, etc. Most of the practical networks are dynamic. A graphlet is a subgraph with a fixed number of vertices and can be induced or non-induced. There are several works for counting graphlets in a static network where graph topology never changes. Surprisingly, there have been no scalable and practical algorithms for maintaining all fixed-sized graphlets in a dynamic network where the graph topology changes over time. We are the first to propose an efficient algorithm for maintaining graphlets in a fully dynamic network. Our algorithm is efficient because (1) we consider only the region of changes in the graph for updating the graphlet count, and (2) we use an efficient algorithm for counting graphlets in the region of change. We show by experimental evaluation that our technique is more than 10x faster than the baseline approach.

翻译：图元计数是一个重要问题，因为它在社交网络分析、生物网络分析、交易网络分析等多个领域有众多应用。大多数实际网络都是动态的。图元是一种具有固定顶点数的子图，可以是导出子图或非导出子图。现有一些工作研究图拓扑结构永不改变的静态网络中的图元计数。令人惊讶的是，对于图拓扑随时间变化的动态网络，目前尚无可扩展且实用的算法来维护所有固定大小的图元。我们首次提出了一种在全动态网络中维护图元的高效算法。我们的算法是高效的，因为：(1) 我们仅考虑图中发生变化区域来更新图元计数，(2) 我们使用高效算法对变化区域内的图元进行计数。实验评估表明，我们的技术比基线方法快10倍以上。