# findCyclicSubgraphs

Find a cycle base of an undirected graph using the Paton's algorithm.

The algorithm is described in

> K. Paton, An algorithm for finding a fundamental set of cycles > for an undirected linear graph, Comm. ACM 12 (1969), pp. 514-518.

and the implementation is adapted from the [Java implementation] of K. Paton originally licensed under [Apache License 2.0].

findCyclicSubgraphs
(
G
)
(
,
G.IncidentEdgesCache incidentEdgesCache = G.IncidentEdgesCache.init
)
if (
is(G : Graph!Params,
Params...
)
)

## Return Value

Type:

range of cycles in the graph represented as arrays of node indices

## Examples

```1 alias G = Graph!int;
2
3 //   __
4 //   \ \
5 //    `-0 -- 1 -- 2 -- 3
6 //      |       / |    |
7 //      |      /  |    |
8 //      4 -- 5 -- 6    7
9 auto g = G([0, 1, 2, 3, 4, 5, 6, 7], [
10     G.edge(0, 0),
11     G.edge(0, 1),
12     G.edge(0, 4),
13     G.edge(1, 2),
14     G.edge(2, 3),
15     G.edge(2, 5),
16     G.edge(2, 6),
17     G.edge(3, 7),
18     G.edge(4, 5),
19     G.edge(5, 6),
20 ]);
21 auto cycles = g.findCyclicSubgraphs();
22
23 import std.algorithm : equal;
24
25 assert(cycles.equal([
26     ,
27     [2, 6, 5],
28     [1, 2, 5, 4, 0],
29 ]));```