Generators for the small graph atlas.
See “An Atlas of Graphs” by Ronald C. Read and Robin J. Wilson, Oxford University Press, 1998.
Because of its size, this module is not imported by default.
| graph_atlas_g() | Return the list [G0,G1,...,G1252] of graphs as named in the Graph Atlas. |
Generators for some classic graphs.
The typical graph generator is called as follows:
>>> G=nx.complete_graph(100)
returning the complete graph on n nodes labeled 0,..,99 as a simple graph. Except for empty_graph, all the generators in this module return a Graph class (i.e. a simple, undirected graph).
| balanced_tree(r, h[, create_using]) | Return the perfectly balanced r-tree of height h. |
| barbell_graph(m1, m2[, create_using]) | Return the Barbell Graph: two complete graphs connected by a path. |
| complete_graph(n[, create_using]) | Return the Complete graph K_n with n nodes. |
| complete_bipartite_graph(n1, n2[, create_using]) | Return the complete bipartite graph K_{n1_n2}. |
| circular_ladder_graph(n[, create_using]) | Return the circular ladder graph CL_n of length n. |
| cycle_graph(n[, create_using]) | Return the cycle graph C_n over n nodes. |
| dorogovtsev_goltsev_mendes_graph(n[, ...]) | Return the hierarchically constructed Dorogovtsev-Goltsev-Mendes graph. |
| empty_graph([n, create_using]) | Return the empty graph with n nodes and zero edges. |
| grid_2d_graph(m, n[, periodic, create_using]) | Return the 2d grid graph of mxn nodes, each connected to its nearest neighbors. |
| grid_graph(dim[, periodic, create_using]) | Return the n-dimensional grid graph. |
| hypercube_graph(n[, create_using]) | Return the n-dimensional hypercube. |
| ladder_graph(n[, create_using]) | Return the Ladder graph of length n. |
| lollipop_graph(m, n[, create_using]) | Return the Lollipop Graph; K_m connected to P_n. |
| null_graph([create_using]) | Return the Null graph with no nodes or edges. |
| path_graph(n[, create_using]) | Return the Path graph P_n of n nodes linearly connected |
| star_graph(n[, create_using]) | Return the Star graph with n+1 nodes: |
| trivial_graph([create_using]) | Return the Trivial graph with one node (with integer label 0) |
| wheel_graph(n[, create_using]) | Return the wheel graph: a single hub node connected to each node of the (n-1)-node cycle graph. |
Various small and named graphs, together with some compact generators.
| make_small_graph(graph_description[, ...]) | Return the small graph described by graph_description. |
| LCF_graph(n, shift_list, repeats[, create_using]) | Return the cubic graph specified in LCF notation. |
| bull_graph([create_using]) | Return the Bull graph. |
| chvatal_graph([create_using]) | Return the Chvatal graph. |
| cubical_graph([create_using]) | Return the 3-regular Platonic Cubical graph. |
| desargues_graph([create_using]) | Return the Desargues graph. |
| diamond_graph([create_using]) | Return the Diamond graph. |
| dodecahedral_graph([create_using]) | Return the Platonic Dodecahedral graph. |
| frucht_graph([create_using]) | Return the Frucht Graph. |
| heawood_graph([create_using]) | Return the Heawood graph, a (3,6) cage. |
| house_graph([create_using]) | Return the House graph (square with triangle on top). |
| house_x_graph([create_using]) | Return the House graph with a cross inside the house square. |
| icosahedral_graph([create_using]) | Return the Platonic Icosahedral graph. |
| krackhardt_kite_graph([create_using]) | Return the Krackhardt Kite Social Network. |
| moebius_kantor_graph([create_using]) | Return the Moebius-Kantor graph. |
| octahedral_graph([create_using]) | Return the Platonic Octahedral graph. |
| pappus_graph() | Return the Pappus graph. |
| petersen_graph([create_using]) | Return the Petersen graph. |
| sedgewick_maze_graph([create_using]) | Return a small maze with a cycle. |
| tetrahedral_graph([create_using]) | Return the 3-regular Platonic Tetrahedral graph. |
| truncated_cube_graph([create_using]) | Return the skeleton of the truncated cube. |
| truncated_tetrahedron_graph([create_using]) | Return the skeleton of the truncated Platonic tetrahedron. |
| tutte_graph([create_using]) | Return the Tutte graph. |
Generators for random graphs.
| fast_gnp_random_graph(n, p[, create_using, seed]) | Return a random graph G_{n,p}. |
| gnp_random_graph(n, p[, create_using, seed]) | Return a random graph G_{n,p}. |
| directed_gnp_random_graph(n, p[, ...]) | Return a directed random graph. |
| dense_gnm_random_graph(n, m[, create_using, ...]) | Return the random graph G_{n,m}. |
| gnm_random_graph(n, m[, create_using, seed]) | Return the random graph G_{n,m}. |
| erdos_renyi_graph(n, p[, create_using, seed]) | Return a random graph G_{n,p}. |
| binomial_graph(n, p[, create_using, seed]) | Return a random graph G_{n,p}. |
| newman_watts_strogatz_graph(n, k, p[, ...]) | Return a Newman-Watts-Strogatz small world graph. |
| watts_strogatz_graph(n, k, p[, ...]) | Return a Watts-Strogatz small-world graph. |
| connected_watts_strogatz_graph(n, k, p[, ...]) | Return a connected Watts-Strogatz small-world graph. |
| random_regular_graph(d, n[, create_using, seed]) | Return a random regular graph of n nodes each with degree d. |
| barabasi_albert_graph(n, m[, create_using, seed]) | Return random graph using Barabási-Albert preferential attachment model. |
| powerlaw_cluster_graph(n, m, p[, ...]) | Holme and Kim algorithm for growing graphs with powerlaw |
| random_lobster(n, p1, p2[, create_using, seed]) | Return a random lobster. |
| random_shell_graph(constructor[, ...]) | Return a random shell graph for the constructor given. |
| random_powerlaw_tree(n[, gamma, ...]) | Return a tree with a powerlaw degree distribution. |
| random_powerlaw_tree_sequence(n[, gamma, ...]) | Return a degree sequence for a tree with a powerlaw distribution. |
Generate graphs with a given degree sequence or expected degree sequence.
| configuration_model(deg_sequence[, ...]) | Return a random graph with the given degree sequence. |
| directed_configuration_model(...[, ...]) | Return a directed_random graph with the given degree sequences. |
| expected_degree_graph(w[, create_using, seed]) | Return a random graph G(w) with expected degrees given by w. |
| havel_hakimi_graph(deg_sequence[, create_using]) | Return a simple graph with given degree sequence, constructed using the |
| degree_sequence_tree(deg_sequence[, ...]) | Make a tree for the given degree sequence. |
| is_valid_degree_sequence(deg_sequence) | Return True if deg_sequence is a valid sequence of integer degrees |
| create_degree_sequence(n, **kwds[, ...]) | Attempt to create a valid degree sequence of length n using specified function sfunction(n,**kwds). |
| double_edge_swap(G[, nswap]) | Attempt nswap double-edge swaps on the graph G. |
| connected_double_edge_swap(G[, nswap]) | Attempt nswap double-edge swaps on the graph G. |
| li_smax_graph(degree_seq[, create_using]) | Generates a graph based with a given degree sequence and maximizing the s-metric. |
Generators for some directed graphs.
gn_graph: growing network gnc_graph: growing network with copying gnr_graph: growing network with redirection scale_free_graph: scale free directed graph
| gn_graph(n[, kernel, create_using, seed]) | Return the GN digraph with n nodes. |
| gnr_graph(n, p[, create_using, seed]) | Return the GNR digraph with n nodes and redirection probability p. |
| gnc_graph(n[, create_using, seed]) | Return the GNC digraph with n nodes. |
| scale_free_graph(n[, alpha, beta, gamma, ...]) | Return a scale free directed graph. |
Generators for geometric graphs.
| random_geometric_graph(n, radius[, ...]) | Random geometric graph in the unit cube |
Hybrid
| kl_connected_subgraph(G, k, l[, low_memory, ...]) | Returns the maximum locally (k,l) connected subgraph of G. |
| is_kl_connected(G, k, l[, low_memory]) | Returns True if G is kl connected |
Generators and functions for bipartite graphs.
| bipartite_configuration_model(aseq, bseq[, ...]) | Return a random bipartite graph from two given degree sequences. |
| bipartite_havel_hakimi_graph(aseq, bseq[, ...]) | Return a bipartite graph from two given degree sequences |
| bipartite_reverse_havel_hakimi_graph(aseq, bseq) | Return a bipartite graph from two given degree sequences |
| bipartite_alternating_havel_hakimi_graph(...) | Return a bipartite graph from two given degree sequences |
| bipartite_preferential_attachment_graph(aseq, p) | Create a bipartite graph with a preferential attachment model from a given single degree sequence. |
| bipartite_random_regular_graph(d, n[, ...]) | UNTESTED: Generate a random bipartite graph. |
Ego graph.
| ego_graph(G, n[, radius, center, undirected]) | Returns induced subgraph of neighbors centered at node n. |
Stocastic graph.
| stochastic_graph(G[, copy]) | Return a right-stochastic representation of G. |