generate_graph.py

# other graphs candidates to check

import networkx as nx
import matplotlib.pyplot as plt
import random

#-> Cycle Graph C8
def cycle_graph_c8():
    G = nx.cycle_graph(8)
    plt.figure(figsize=(6, 6))
    pos = nx.circular_layout(G)
    nx.draw(G, pos, with_labels=True, node_color='lightblue', edge_color='gray', node_size=500)
    plt.title("Cycle Graph C8")
    plt.show()
    return G

# Path Graph P16
def path_graph_p16():
    G = nx.path_graph(16)
    plt.figure(figsize=(12, 2))
    pos = nx.spring_layout(G, seed=42)
    nx.draw(G, pos, with_labels=True, node_color='lightgreen', edge_color='gray', node_size=300)
    plt.title("Path Graph P16")
    plt.show()
    return G

#-> Complete Bipartite Graph K8,8
def complete_bipartite_graph_k88():
    G = nx.complete_bipartite_graph(8, 8)
    plt.figure(figsize=(8, 6))
    pos = nx.bipartite_layout(G, nodes=range(8))
    nx.draw(G, pos, with_labels=True, node_color=['lightcoral'] * 8 + ['lightblue'] * 8,
            edge_color='gray', node_size=300)
    plt.title("Complete Bipartite Graph K8,8")
    plt.show()
    return G

#-> Complete Bipartite Graph K8,8
def complete_bipartite_graph_k_nn(n):
    G = nx.complete_bipartite_graph(n, n)
    plt.figure(figsize=(8, 6))
    pos = nx.bipartite_layout(G, nodes=range(n))
    nx.draw(G, pos, with_labels=True, node_color=['lightcoral'] * n + ['lightblue'] * n,
            edge_color='gray', node_size=300)
    plt.title("Complete Bipartite Graph K{},{}".format(n,n))
    plt.show()
    return G

# Star Graph S16
def star_graph_s16():
    G = nx.star_graph(16)
    plt.figure(figsize=(8, 8))
    pos = nx.spring_layout(G, seed=42)
    nx.draw(G, pos, with_labels=True, node_color='gold', edge_color='gray', node_size=300)
    plt.title("Star Graph S16")
    plt.show()
    return G

# Grid Graph 8x4
def grid_graph_8x4():
    G = nx.grid_graph(dim=[8, 4])
    plt.figure(figsize=(12, 6))
    pos = {node: node for node in G.nodes()}
    nx.draw(G, pos, with_labels=True, node_color='lightblue', edge_color='gray', node_size=300)
    plt.title("Grid Graph 8x4")
    plt.show()
    return G

# Grid Graph 8x4
def grid_graph_nxm(n,m):
    G = nx.grid_graph(dim=[n, m])
    plt.figure(figsize=(12, 6))
    pos = {node: node for node in G.nodes()}
    nx.draw(G, pos, with_labels=True, node_color='lightblue', edge_color='gray', node_size=300)
    plt.title("Grid Graph {}x{}".format(n,m))
    plt.show()
    return G


#-> 4-Regular Graph with 8 Vertices
def regular_graph_4_8():
    G = nx.random_regular_graph(d=4, n=8, seed=42)
    plt.figure(figsize=(6, 6))
    pos = nx.circular_layout(G)
    nx.draw(G, pos, with_labels=True, node_color='lightgreen', edge_color='gray', node_size=500)
    plt.title("4-Regular Graph with 8 Vertices")
    plt.show()
    return G

#-> Cubic (3-Regular) Graph with 16 Vertices
def cubic_graph_3_16():
    G = nx.random_regular_graph(d=3, n=16, seed=42)
    plt.figure(figsize=(8, 6))
    pos = nx.spring_layout(G, seed=42)
    nx.draw(G, pos, with_labels=True, node_color='lightcoral', edge_color='gray', node_size=300)
    plt.title("Cubic (3-Regular) Graph with 16 Vertices")
    plt.show()
    return G

# Disjoint Union of Four C4 Cycles
def disjoint_union_c4():
    cycles = [nx.cycle_graph(4) for _ in range(4)]
    G = nx.disjoint_union_all(cycles)
    plt.figure(figsize=(12, 6))
    pos = {}
    shift_x = 0
    for component in nx.connected_components(G):
        subgraph = G.subgraph(component)
        pos_sub = nx.circular_layout(subgraph, scale=1, center=(shift_x, 0))
        pos.update(pos_sub)
        shift_x += 3
    nx.draw(G, pos, with_labels=True, node_color='lightblue', edge_color='gray', node_size=300)
    plt.title("Disjoint Union of Four C4 Cycles")
    plt.show()
    return G

# Complete Bipartite Graph K16,16
def complete_bipartite_graph_k1616():
    G = nx.complete_bipartite_graph(16, 16)
    plt.figure(figsize=(12, 6))
    pos = nx.bipartite_layout(G, nodes=range(16))
    nx.draw(G, pos, with_labels=False, node_color=['lightcoral'] * 16 + ['lightblue'] * 16,
            edge_color='gray', node_size=100)
    plt.title("Complete Bipartite Graph K16,16")
    plt.show()
    return G

# 5-Dimensional Hypercube Graph Q5
def hypercube_graph_q5():
    G = nx.hypercube_graph(5)
    plt.figure(figsize=(10, 8))
    pos = nx.spring_layout(G, seed=42)
    nx.draw(G, pos, with_labels=False, node_color='lightgreen', edge_color='gray', node_size=200)
    plt.title("5-Dimensional Hypercube Graph Q5")
    plt.show()
    return G

# Tree Graph with 8 Vertices
def tree_graph_8():
    G = nx.balanced_tree(r=2, h=2)
    G.add_edge(6, 7)
    plt.figure(figsize=(8, 6))
    pos = nx.spring_layout(G, seed=42)
    nx.draw(G, pos, with_labels=True, node_color='lightblue', edge_color='gray', node_size=300)
    plt.title("Tree Graph with 8 Vertices")
    plt.show()
    return G

# Wheel Graph W16
def wheel_graph_w16():
    G = nx.wheel_graph(16)
    plt.figure(figsize=(8, 8))
    pos = nx.circular_layout(G)
    nx.draw(G, pos, with_labels=True, node_color='lightcoral', edge_color='gray', node_size=300)
    plt.title("Wheel Graph W16")
    plt.show()
    return G

#-> Random Connected Graph with 16 Vertices
def random_connected_graph_16(p=0.15):
    #n, p = 16, 0.25
    n=16
    while True:
        G = nx.erdos_renyi_graph(n, p, seed=random.randint(1, 10000))
        if nx.is_connected(G):
            break
    plt.figure(figsize=(10, 8))
    pos = nx.spring_layout(G, seed=42)
    nx.draw(G, pos, with_labels=False, node_color='lightgreen', edge_color='gray', node_size=100)
    plt.title("Random Connected Graph with 16 Vertices")
    plt.show()
    return G

# Expander Graph with 32 Vertices
def expander_graph_32():
    G = nx.random_regular_graph(4, 32, seed=42)
    plt.figure(figsize=(10, 8))
    pos = nx.spring_layout(G, seed=42)
    nx.draw(G, pos, with_labels=False, node_color='lightblue', edge_color='gray', node_size=100)
    plt.title("Expander Graph with 32 Vertices")
    plt.show()
    return G

#-> Expander Graph with n Vertices
def expander_graph_n(n):
    G = nx.random_regular_graph(4, n, seed=42)
    plt.figure(figsize=(10, 8))
    pos = nx.spring_layout(G, seed=42)
    nx.draw(G, pos, with_labels=False, node_color='lightblue', edge_color='gray', node_size=100)
    plt.title("Expander Graph with {} Vertices".format(n))
    plt.show()
    return G

# Planar Connected Graph with 16 Vertices
def planar_connected_graph_16():
    G = nx.grid_graph(dim=[8, 2])
    G = nx.convert_node_labels_to_integers(G)
    additional_edges = [(0, 9), (1, 10), (2, 11), (3, 12), (4, 13), (5, 14), (6, 15),
                        (7, 15), (8, 7)]#, (6, 15), (14, 1), (1, 13), (10, 9), (0, 10), (12, 2), (8, 7)]
    G.add_edges_from([e for e in additional_edges if e[0] < 16 and e[1] < 16])
    assert nx.check_planarity(G)[0], "Graph is not planar."
    pos = {node: (node // 2, node % 2) for node in G.nodes()}
    plt.figure(figsize=(16, 8))
    nx.draw(G, pos, with_labels=False, node_color='lightcoral', edge_color='gray', node_size=100)
    plt.title("Planar Connected Graph with 16 Vertices")
    plt.axis('equal')
    plt.show()
    return G