CXXGraph库提供了一组检测周期的算法和函数。

要获得完整的算法解释，请访问wiki。

CXXGraph库提供了一组检测周期的算法和函数。

要获得完整的算法解释，请访问wiki。

在DAG中查找所有循环涉及两个步骤(算法)。

第一步是使用Tarjan的算法找到强连接组件的集合。

从任意顶点开始。 这个顶点的DFS。每个节点x保留两个数字，dfs_index[x]和dfs_lowval[x]。 Dfs_index [x]存储访问节点的时间，而dfs_lowval[x] = min(dfs_low[k]) where K是x的所有子结点在dfs生成树中不是x的父结点。 具有相同dfs_lowval[x]的所有节点都在同一个强连接组件中。

第二步是在连接的组件中找到循环(路径)。我的建议是使用改进版的Hierholzer算法。

这个想法是:

Choose any starting vertex v, and follow a trail of edges from that vertex until you return to v. It is not possible to get stuck at any vertex other than v, because the even degree of all vertices ensures that, when the trail enters another vertex w there must be an unused edge leaving w. The tour formed in this way is a closed tour, but may not cover all the vertices and edges of the initial graph. As long as there exists a vertex v that belongs to the current tour but that has adjacent edges not part of the tour, start another trail from v, following unused edges until you return to v, and join the tour formed in this way to the previous tour.

下面是带有测试用例的Java实现的链接:

http://stones333.blogspot.com/2013/12/find-cycles-in-directed-graph-dag.html

澄清:

Strongly Connected Components will find all subgraphs that have at least one cycle in them, not all possible cycles in the graph. e.g. if you take all strongly connected components and collapse/group/merge each one of them into one node (i.e. a node per component), you'll get a tree with no cycles (a DAG actually). Each component (which is basically a subgraph with at least one cycle in it) can contain many more possible cycles internally, so SCC will NOT find all possible cycles, it will find all possible groups that have at least one cycle, and if you group them, then the graph will not have cycles. to find all simple cycles in a graph, as others mentioned, Johnson's algorithm is a candidate.

我无意中发现了下面的算法，它似乎比Johnson的算法更有效(至少对于更大的图)。然而，与Tarjan的算法相比，我不确定它的性能如何。 此外，到目前为止，我只检查了三角形。如果感兴趣，请参阅千叶Norishige和西泽木高雄(http://dx.doi.org/10.1137/0214017)的“树状性和子图列表算法”

http://www.me.utexas.edu/~bard/IP/Handouts/cycles.pdf