# Graph generators¶

## Classic¶

 balanced_tree(r, h[, create_using]) Returns the perfectly balanced r-ary tree of height h. barbell_graph(m1, m2[, create_using]) Returns the Barbell Graph: two complete graphs connected by a path. Returns the Binomial Tree of order n. complete_graph(n[, create_using]) Return the complete graph K_n with n nodes. complete_multipartite_graph(*subset_sizes) Returns the complete multipartite graph with the specified subset sizes. circular_ladder_graph(n[, create_using]) Returns the circular ladder graph $CL_n$ of length n. circulant_graph(n, offsets[, create_using]) Generates the circulant graph $Ci_n(x_1, x_2, …, x_m)$ with $n$ vertices. cycle_graph(n[, create_using]) Returns the cycle graph $C_n$ of cyclically connected nodes. Returns the hierarchically constructed Dorogovtsev-Goltsev-Mendes graph. empty_graph([n, create_using, default]) Returns the empty graph with n nodes and zero edges. full_rary_tree(r, n[, create_using]) Creates a full r-ary tree of n vertices. ladder_graph(n[, create_using]) Returns the Ladder graph of length n. lollipop_graph(m, n[, create_using]) Returns the Lollipop Graph; K_m connected to P_n. null_graph([create_using]) Returns the Null graph with no nodes or edges. path_graph(n[, create_using]) Returns the Path graph P_n of linearly connected nodes. star_graph(n[, create_using]) Return the star graph trivial_graph([create_using]) Return the Trivial graph with one node (with label 0) and no edges. turan_graph(n, r) Return the Turan Graph wheel_graph(n[, create_using]) Return the wheel graph

## Social Networks¶

 Returns Zachary’s Karate Club graph. Returns Davis Southern women social network. Returns Florentine families graph. Returns coappearance network of characters in the novel Les Miserables.