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TODO
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Note that these are possibilities, not plans nor promises.
- graph periphery: the subgraph of graph center vertices
- finding the shortest cycle: easy for directed (*), but how about undirected?
(*) http://www.cs.auckland.ac.nz/~ute/220ft/graphalg/node14.html
do a BFS, when sees an already seen vertex, a cycle of length of at most
twice the current depth of the BFS has been found; no cycles => V + 1 (Inf)
- bipartite aka 2-colourable: again, BFS:
http://www.cs.auckland.ac.nz/~ute/220ft/graphalg/node15.html
- Eulerian circuit: Fleury's algorithm:
http://planetmath.org/encyclopedia/FleurysAlgorithm.html
- could_be_isomorphic() - go second degree?
1. separate external and internal attributes?
2. biconn: add next_root
3. DAG SSSP
4. flow: Ford-Fulkerson/Edmonds-Karp/preflow-push? Floyd-Warshall variant?
-- Classics --
Undirected graphs
- connectivity
- given two vertices are they on a cycle
- find_all_paths($u, $v)?
- find_all_cycles()? NP-complete; equivalent to finding all Hamiltonians
- Euler tour
Digraphs
- disallow_selfloops => 1?
- odd-length cycle
- shortest paths (bfs)
- squaring a graph: for (u,v)(v,w) add (u,w) unless already there
- graph union, graph difference?
Various specialized graph constructors?
- n-dim grid (with wraps and connectors -> wheels (webs), cones),
circle, star, platonic solids, trees, etc.