Generates a complete binary tree of given depth.

A complete binary tree where:

• Node 0 is the root
• For node i: left child is 2i+1, right child is 2i+2
• Total nodes: 2^(depth+1) - 1

All edges have unit weight (1).

Time Complexity: O(2^depth)

Example

let tree = generate.binary_tree(3)
// Creates a binary tree with 15 nodes (depth 3)
//        0
//      /   \
//     1     2
//    / \   / \
//   3   4 5   6
//  /|\ /|\ ...

Generates a complete binary tree with specified graph type.

Generates a complete graph K_n where every node is connected to every other node.

In a complete graph with n nodes, there are n(n-1)/2 edges for undirected graphs and n(n-1) edges for directed graphs.

All edges have unit weight (1).

Time Complexity: O(n²)

Example

let k5 = generate.complete(5)
// Creates a complete graph with 5 nodes
// Each node connected to all other 4 nodes

Generates a complete bipartite graph K_{m,n}.

A complete bipartite graph has two partitions of nodes where every node in the first partition is connected to every node in the second partition.

Nodes 0 to m-1 form the left partition. Nodes m to m+n-1 form the right partition.

All edges have unit weight (1).

Time Complexity: O(mn)

Example

let k33 = generate.complete_bipartite(3, 3)
// Nodes 0,1,2 on left, nodes 3,4,5 on right
// All left nodes connected to all right nodes

Generates a complete bipartite graph with specified graph type.

Generates a complete graph with specified graph type.

Example

let directed_k4 = generate.complete_with_type(4, model.Directed)

Generates a cycle graph C_n where nodes form a ring.

A cycle graph connects n nodes in a circular pattern: 0 -> 1 -> 2 -> … -> (n-1) -> 0

All edges have unit weight (1).

Time Complexity: O(n)

Example

let c6 = generate.cycle(6)
// Creates a cycle: 0-1-2-3-4-5-0

Generates a cycle graph with specified graph type.

Generates an empty graph with n nodes and no edges.

Useful as a starting point for custom graph construction.

Time Complexity: O(n)

Example

let empty = generate.empty(10)
// 10 isolated nodes, no edges

Generates an empty graph with specified graph type.

Generates a 2D grid graph (lattice).

Creates a grid of rows × cols nodes arranged in a rectangular lattice. Each internal node has 4 neighbors (up, down, left, right). Edge nodes have fewer neighbors.

Node IDs are assigned row-major: node_id = row * cols + col

All edges have unit weight (1).

Time Complexity: O(rows * cols)

Example

let grid = generate.grid_2d(3, 4)
// Creates a 3×4 grid:
//   0 - 1 - 2 - 3
//   |   |   |   |
//   4 - 5 - 6 - 7
//   |   |   |   |
//   8 - 9 -10 -11

Generates a 2D grid graph with specified graph type.

Generates a path graph P_n where nodes form a linear chain.

A path graph connects n nodes in a line: 0 - 1 - 2 - … - (n-1)

All edges have unit weight (1).

Time Complexity: O(n)

Example

let p5 = generate.path(5)
// Creates a path: 0-1-2-3-4

Generates a path graph with specified graph type.

Generates a Petersen graph.

The Petersen graph is a famous graph in graph theory, often used as a counterexample. It has 10 nodes and 15 edges, and is non-planar.

All edges have unit weight (1).

Time Complexity: O(1) - fixed size

Example

let petersen = generate.petersen()
// Creates the classic Petersen graph with 10 nodes

Generates a Petersen graph with specified graph type.

Generates a star graph where one central node is connected to all others.

Node 0 is the center, connected to nodes 1 through n-1. A star with n nodes has n-1 edges.

All edges have unit weight (1).

Time Complexity: O(n)

Example

let s6 = generate.star(6)
// Center node 0 connected to nodes 1, 2, 3, 4, 5

Generates a star graph with specified graph type.

Generates a wheel graph: a cycle with a central hub.

A wheel graph is a cycle of n-1 nodes with an additional central node connected to all nodes in the cycle.

Node 0 is the center, nodes 1 through n-1 form the cycle.

All edges have unit weight (1).

Time Complexity: O(n)

Example

let w6 = generate.wheel(6)
// Center node 0, cycle 1-2-3-4-5-1, center connected to all

Generates a wheel graph with specified graph type.