8.0 KiB
8.0 KiB
NetworkX Graph Generators
Classic Graphs
Complete Graphs
# Complete graph (all nodes connected to all others)
G = nx.complete_graph(n=10)
# Complete bipartite graph
G = nx.complete_bipartite_graph(n1=5, n2=7)
# Complete multipartite graph
G = nx.complete_multipartite_graph(3, 4, 5) # Three partitions
Cycle and Path Graphs
# Cycle graph (nodes arranged in circle)
G = nx.cycle_graph(n=20)
# Path graph (linear chain)
G = nx.path_graph(n=15)
# Circular ladder graph
G = nx.circular_ladder_graph(n=10)
Regular Graphs
# Empty graph (no edges)
G = nx.empty_graph(n=10)
# Null graph (no nodes)
G = nx.null_graph()
# Star graph (one central node connected to all others)
G = nx.star_graph(n=19) # Creates 20-node star
# Wheel graph (cycle with central hub)
G = nx.wheel_graph(n=10)
Special Named Graphs
# Bull graph
G = nx.bull_graph()
# Chvatal graph
G = nx.chvatal_graph()
# Cubical graph
G = nx.cubical_graph()
# Diamond graph
G = nx.diamond_graph()
# Dodecahedral graph
G = nx.dodecahedral_graph()
# Heawood graph
G = nx.heawood_graph()
# House graph
G = nx.house_graph()
# Petersen graph
G = nx.petersen_graph()
# Karate club graph (classic social network)
G = nx.karate_club_graph()
Random Graphs
Erdős-Rényi Graphs
# G(n, p) model: n nodes, edge probability p
G = nx.erdos_renyi_graph(n=100, p=0.1, seed=42)
# G(n, m) model: n nodes, exactly m edges
G = nx.gnm_random_graph(n=100, m=500, seed=42)
# Fast version (for large sparse graphs)
G = nx.fast_gnp_random_graph(n=10000, p=0.0001, seed=42)
Watts-Strogatz Small-World
# Small-world network with rewiring
# n nodes, k nearest neighbors, rewiring probability p
G = nx.watts_strogatz_graph(n=100, k=6, p=0.1, seed=42)
# Connected version (guarantees connectivity)
G = nx.connected_watts_strogatz_graph(n=100, k=6, p=0.1, tries=100, seed=42)
Barabási-Albert Preferential Attachment
# Scale-free network (power-law degree distribution)
# n nodes, m edges to attach from new node
G = nx.barabasi_albert_graph(n=100, m=3, seed=42)
# Extended version with parameters
G = nx.extended_barabasi_albert_graph(n=100, m=3, p=0.5, q=0.2, seed=42)
Power Law Degree Sequence
# Power law cluster graph
G = nx.powerlaw_cluster_graph(n=100, m=3, p=0.1, seed=42)
# Random power law tree
G = nx.random_powerlaw_tree(n=100, gamma=3, seed=42, tries=1000)
Configuration Model
# Graph with specified degree sequence
degree_sequence = [3, 3, 3, 3, 2, 2, 2, 1, 1, 1]
G = nx.configuration_model(degree_sequence, seed=42)
# Remove self-loops and parallel edges
G = nx.Graph(G)
G.remove_edges_from(nx.selfloop_edges(G))
Random Geometric Graphs
# Nodes in unit square, edges if distance < radius
G = nx.random_geometric_graph(n=100, radius=0.2, seed=42)
# With positions
pos = nx.get_node_attributes(G, 'pos')
Random Regular Graphs
# Every node has exactly d neighbors
G = nx.random_regular_graph(d=3, n=100, seed=42)
Stochastic Block Model
# Community structure model
sizes = [50, 50, 50] # Three communities
probs = [[0.25, 0.05, 0.02], # Within and between community probabilities
[0.05, 0.35, 0.07],
[0.02, 0.07, 0.40]]
G = nx.stochastic_block_model(sizes, probs, seed=42)
Lattice and Grid Graphs
Grid Graphs
# 2D grid
G = nx.grid_2d_graph(m=5, n=7) # 5x7 grid
# 3D grid
G = nx.grid_graph(dim=[5, 7, 3]) # 5x7x3 grid
# Hexagonal lattice
G = nx.hexagonal_lattice_graph(m=5, n=7)
# Triangular lattice
G = nx.triangular_lattice_graph(m=5, n=7)
Hypercube
# n-dimensional hypercube
G = nx.hypercube_graph(n=4)
Tree Graphs
Random Trees
# Random tree with n nodes
G = nx.random_tree(n=100, seed=42)
# Prefix tree (tries)
G = nx.prefix_tree([[0, 1, 2], [0, 1, 3], [0, 4]])
Balanced Trees
# Balanced r-ary tree of height h
G = nx.balanced_tree(r=2, h=5) # Binary tree, height 5
# Full r-ary tree with n nodes
G = nx.full_rary_tree(r=3, n=100) # Ternary tree
Barbell and Lollipop Graphs
# Two complete graphs connected by path
G = nx.barbell_graph(m1=5, m2=3) # Two K_5 graphs with 3-node path
# Complete graph connected to path
G = nx.lollipop_graph(m=7, n=5) # K_7 with 5-node path
Social Network Models
Karate Club
# Zachary's karate club (classic social network)
G = nx.karate_club_graph()
Davis Southern Women
# Bipartite social network
G = nx.davis_southern_women_graph()
Florentine Families
# Historical marriage and business networks
G = nx.florentine_families_graph()
Les Misérables
# Character co-occurrence network
G = nx.les_miserables_graph()
Directed Graph Generators
Random Directed Graphs
# Directed Erdős-Rényi
G = nx.gnp_random_graph(n=100, p=0.1, directed=True, seed=42)
# Scale-free directed
G = nx.scale_free_graph(n=100, seed=42)
DAG (Directed Acyclic Graph)
# Random DAG
G = nx.gnp_random_graph(n=20, p=0.2, directed=True, seed=42)
G = nx.DiGraph([(u, v) for (u, v) in G.edges() if u < v]) # Remove backward edges
Tournament Graphs
# Random tournament (complete directed graph)
G = nx.random_tournament(n=10, seed=42)
Duplication-Divergence Models
Duplication Divergence Graph
# Biological network model (protein interaction networks)
G = nx.duplication_divergence_graph(n=100, p=0.5, seed=42)
Degree Sequence Generators
Valid Degree Sequences
# Check if degree sequence is valid (graphical)
sequence = [3, 3, 3, 3, 2, 2, 2, 1, 1, 1]
is_valid = nx.is_graphical(sequence)
# For directed graphs
in_sequence = [2, 2, 2, 1, 1]
out_sequence = [2, 2, 1, 2, 1]
is_valid = nx.is_digraphical(in_sequence, out_sequence)
Creating from Degree Sequence
# Havel-Hakimi algorithm
G = nx.havel_hakimi_graph(degree_sequence)
# Configuration model (allows multi-edges/self-loops)
G = nx.configuration_model(degree_sequence)
# Directed configuration model
G = nx.directed_configuration_model(in_degree_sequence, out_degree_sequence)
Bipartite Graphs
Random Bipartite
# Random bipartite with two node sets
G = nx.bipartite.random_graph(n=50, m=30, p=0.1, seed=42)
# Configuration model for bipartite
G = nx.bipartite.configuration_model(deg1=[3, 3, 2], deg2=[2, 2, 2, 2], seed=42)
Bipartite Generators
# Complete bipartite
G = nx.complete_bipartite_graph(n1=5, n2=7)
# Gnmk random bipartite (n, m nodes, k edges)
G = nx.bipartite.gnmk_random_graph(n=10, m=8, k=20, seed=42)
Operators on Graphs
Graph Operations
# Union
G = nx.union(G1, G2)
# Disjoint union
G = nx.disjoint_union(G1, G2)
# Compose (overlay)
G = nx.compose(G1, G2)
# Complement
G = nx.complement(G1)
# Cartesian product
G = nx.cartesian_product(G1, G2)
# Tensor (Kronecker) product
G = nx.tensor_product(G1, G2)
# Strong product
G = nx.strong_product(G1, G2)
Customization and Seeding
Setting Random Seed
Always set seed for reproducible graphs:
G = nx.erdos_renyi_graph(n=100, p=0.1, seed=42)
Converting Graph Types
# Convert to specific type
G_directed = G.to_directed()
G_undirected = G.to_undirected()
G_multi = nx.MultiGraph(G)
Performance Considerations
Fast Generators
For large graphs, use optimized generators:
# Fast ER graph (sparse)
G = nx.fast_gnp_random_graph(n=10000, p=0.0001, seed=42)
Memory Efficiency
Some generators create graphs incrementally to save memory. For very large graphs, consider:
- Using sparse representations
- Generating subgraphs as needed
- Working with adjacency lists or edge lists instead of full graphs
Validation and Properties
Checking Generated Graphs
# Verify properties
print(f"Nodes: {G.number_of_nodes()}")
print(f"Edges: {G.number_of_edges()}")
print(f"Density: {nx.density(G)}")
print(f"Connected: {nx.is_connected(G)}")
# Degree distribution
degree_sequence = sorted([d for n, d in G.degree()], reverse=True)