Mining subgraphs with interesting structural properties from networks (or graphs) is a computationally challenging task. In this paper, we propose two algorithms for enumerating all connected induced subgraphs of a given cardinality from networks (or connected undirected graphs in networks). The first algorithm is a variant of a previous well-known algorithm. The algorithm enumerates all connected induced subgraphs of cardinality $k$ in a bottom-up manner. The data structures that lead to unit time element checking and linear space are presented. Different from previous algorithms that either work in a bottom-up manner or a reverse search manner, an algorithm that enumerates all connected induced subgraphs of cardinality $k$ in a top-down manner is proposed. The correctness and complexity of the top-down algorithm are theoretically analyzed and proven. In the experiments, we evaluate the efficiency of the algorithms using a set of real-world networks from various fields. Experimental results show that the variant bottom-up algorithm outperforms the state-of-the-art algorithms for enumerating connected induced subgraphs of small cardinality, and the top-down algorithm can achieve an order of magnitude speedup over the state-of-the-art algorithms for enumerating connected induced subgraphs of large cardinality.
翻译:具有网络( 或图形) 中有趣的结构属性的采矿子图是一个具有进化挑战性的任务。 在本文中, 我们提出两个算法, 用来从网络( 或网络中未连接的图表) 中列出所有连接的引出的基本人物( 或网络中未连接的图表) 。 第一个算法是以前众所周知的算法的变体。 算法以自下而上的方式列出了所有连接的基点( 或图形) 的子集。 算法以自下而上的方式列出了所有连接的引出的基本人物( 或网络中未连接的图表) 。 算法以自下而上的方式列出了所有连接的基点( 或图) 的子集 。 实验结果显示, 导致单位时间元素检查和线性空间的数据结构不同。 不同于以自下而上而起的方式工作或逆向搜索方式计算的所有前算法, 以自上而下而上而下的方式列出所有连接的主要基本人物( $ k$ ) 的子集, 和自上而下而下而上而上而上之的算的算算法数字可以实现一个大的规模。</s>