Package: graphtheory
graphtheory packagePython implementation of graph data structures and algorithms is presented.
The minimal graph interface is defined together with several
classes implementing this interface.
Graph nodes can be any hashable Python objects.
Directed edges are instances of the Edge class.
Graphs are instances of the Graph class (several versions).
Multigraphs are instances of the MultiGraph class.
Many algorithms are implemented using a unified approach.
There are separate classes and modules devoted to different algorithms.Problems and algorithmsConnectivity: connected components, strongly connected components,
cut nodes, cut edges (bridges)Cycle detection, topological sorting (DFS, Kahn),
transitive closure (matrix multiplication, Floyd-Warshall, BFS, DFS)Bipartiteness: bipartite graphs detection (BFS, DFS),
maximum-cardinality matching (Hopcroft-Karp, Ford-Fulkerson)Matching: heuristics (greedy for a maximal cardinality matching,
greedy for a minimum weight matching)Vertex coloring: sequential (US, RS, CS),
Brooks' theorem (Delta colors),
m-coloring (backtracking, exact),
counter method (exact),
LF, SLF, RLF, SL, GISEdge coloring: with the line graph (using vertex coloring),
sequential (US, RS, CS),
NTL (using Delta or Delta+1 colors),
complete graphs (exact),
bipartite graphs (exact)Independent sets: backtracking (exact), US, RS, LL, SFDominating sets: backtracking (exact), hybrid (exact), US, RS, LFVertex covers (heuristics): greedy, 2-approximation, LFMinimum spanning trees (weighted undirected graphs):
Boruvka, Prim, KruskalSingle-source shortest paths (weighted directed graphs without negative cycles):
Dijkstra (nonnegative weights), DAGs (using topological sorting),
Bellman-FordAll-pairs shortest paths (weighted directed graphs without negative cycles):
Floyd-Warshall, Johnson, matrix multiplicationsEulerian graphs: DFS, Fleury, HierholzerHamiltonian graphs: DFS, tournaments,
TSP (DFS, with MST, NN, RNN, sorted edges)Forests (exact algorithms): iset, dset, vertex cover, matching,
tree center, longest path problem, plottingUndirected series-parallel graphs (exact algorithms): recognition, generators,
iset, dset, vertex cover, matching,
chordal completion (PEO), vertex coloringDirected series-parallel graphs: recognition, generatorsHalin graphs (exact algorithms): recognition, generators, vertex coloring,
chordal completion (PEO), tree decomposition, plottingChordal graphs (exact algorithms): recognition, generators,
finding PEO (MCS),
finding maximum clique (PEO, MDO),
finding all maximal cliques (PEO),
finding maximum independent set (PEO),
finding tree decomposition (TD),
finding minimum dominating set (TD),
finding minimum node cover (TD)Interval graphs: double perm representation, generators,
traversing (BFS, DFS),
finding path decompositionOuterplanar graphs (exact algorithms): recognition,
chordal completion (PEO), vertex coloringPermutation graphs: generators,
traversing (BFS, DFS) O(n^2),
connectivity O(n)Circle graphs: double perm representation, generators,
traversing (BFS, DFS) O(n^2),
connectivity O(n^2)Clustering: KruskalDownloadTo install an official release dopython3 -m pip install graphtheoryTo get the git version dogit clone https://github.com/ufkapano/graphtheory.gitUsageSee doc/quickstart.txt and other doc/*.txt files.References[1] A. Kapanowski and Ł. Gałuszka,Weighted graph algorithms with Python.http://arxiv.org/abs/1504.07828[draft]A. Kapanowski and Ł. Gałuszka,Weighted graph algorithms with Python.
The Python Papers 11, 3 (2016).http://ojs.pythonpapers.org/index.php/tpp/article/view/270[final version][2] A. Kapanowski and A. Krawczyk,Halin graphs are 3-vertex-colorable except even wheels.https://arxiv.org/abs/1903.02904ContributorsAndrzej Kapanowski (project leader)Łukasz Gałuszka (MST, shortest paths, flows)Łukasz Malinowski (matching, Eulerian graphs, graph coloring, bipartite graphs)Paweł Motyl (multigraphs, graph coloring, independent sets)Piotr Szestało (Hamiltonian graphs, TSP, tournaments)Kacper Dziubek (planarity testing)Sandra Pażyniowska (graph drawing)Wojciech Sarka (dominating sets)Igor Samson (graph coloring)Dariusz Zdybski (cliques)Aleksander Krawczyk (Halin graphs, wheel graphs)Małgorzata Olak (chordal graphs)Krzysztof Niedzielski (matching)Konrad Gałuszka (series-parallel graphs)Maciej Niezabitowski (tree decomposition)Piotr Wlazło (edge coloring)Magdalena Stępień (planar graphs)Sandra Rudnicka (outerplanar graphs)Albert Surmacz (permutation graphs, circle graphs)Maciej Mularski (interval graphs)Angelika Siwek (AT-free graphs)Honorata Zych (chordal completion)EOF