gh-k-dense-ai-claude-scientific-skills-scientific-skills/skills/networkx/references/graph-basics.md

NetworkX Graph Basics

Graph Types

NetworkX supports four main graph classes:

Graph (Undirected)

import networkx as nx
G = nx.Graph()

• Undirected graphs with single edges between nodes
• No parallel edges allowed
• Edges are bidirectional

DiGraph (Directed)

G = nx.DiGraph()

• Directed graphs with one-way connections
• Edge direction matters: (u, v) ≠ (v, u)
• Used for modeling directed relationships

MultiGraph (Undirected Multi-edge)

G = nx.MultiGraph()

• Allows multiple edges between same node pairs
• Useful for modeling multiple relationships

MultiDiGraph (Directed Multi-edge)

G = nx.MultiDiGraph()

• Directed graph with multiple edges between nodes
• Combines features of DiGraph and MultiGraph

Creating and Adding Nodes

Single Node Addition

G.add_node(1)
G.add_node("protein_A")
G.add_node((x, y))  # Nodes can be any hashable type

Bulk Node Addition

G.add_nodes_from([2, 3, 4])
G.add_nodes_from(range(100, 110))

Nodes with Attributes

G.add_node(1, time='5pm', color='red')
G.add_nodes_from([
    (4, {"color": "red"}),
    (5, {"color": "blue", "weight": 1.5})
])

Important Node Properties

• Nodes can be any hashable Python object: strings, tuples, numbers, custom objects
• Node attributes stored as key-value pairs
• Use meaningful node identifiers for clarity

Creating and Adding Edges

Single Edge Addition

G.add_edge(1, 2)
G.add_edge('gene_A', 'gene_B')

Bulk Edge Addition

G.add_edges_from([(1, 2), (1, 3), (2, 4)])
G.add_edges_from(edge_list)

Edges with Attributes

G.add_edge(1, 2, weight=4.7, relation='interacts')
G.add_edges_from([
    (1, 2, {'weight': 4.7}),
    (2, 3, {'weight': 8.2, 'color': 'blue'})
])

Adding from Edge List with Attributes

# From pandas DataFrame
import pandas as pd
df = pd.DataFrame({'source': [1, 2], 'target': [2, 3], 'weight': [4.7, 8.2]})
G = nx.from_pandas_edgelist(df, 'source', 'target', edge_attr='weight')

Examining Graph Structure

Basic Properties

# Get collections
G.nodes              # NodeView of all nodes
G.edges              # EdgeView of all edges
G.adj                # AdjacencyView for neighbor relationships

# Count elements
G.number_of_nodes()  # Total node count
G.number_of_edges()  # Total edge count
len(G)              # Number of nodes (shorthand)

# Degree information
G.degree()          # DegreeView of all node degrees
G.degree(1)         # Degree of specific node
list(G.degree())    # List of (node, degree) pairs

Checking Existence

# Check if node exists
1 in G              # Returns True/False
G.has_node(1)

# Check if edge exists
G.has_edge(1, 2)

Accessing Neighbors

# Get neighbors of node 1
list(G.neighbors(1))
list(G[1])          # Dictionary-like access

# For directed graphs
list(G.predecessors(1))  # Incoming edges
list(G.successors(1))    # Outgoing edges

Iterating Over Elements

# Iterate over nodes
for node in G.nodes:
    print(node, G.nodes[node])  # Access node attributes

# Iterate over edges
for u, v in G.edges:
    print(u, v, G[u][v])  # Access edge attributes

# Iterate with attributes
for node, attrs in G.nodes(data=True):
    print(node, attrs)

for u, v, attrs in G.edges(data=True):
    print(u, v, attrs)

Modifying Graphs

Removing Elements

# Remove single node (also removes incident edges)
G.remove_node(1)

# Remove multiple nodes
G.remove_nodes_from([1, 2, 3])

# Remove edges
G.remove_edge(1, 2)
G.remove_edges_from([(1, 2), (2, 3)])

Clearing Graph

G.clear()           # Remove all nodes and edges
G.clear_edges()     # Remove only edges, keep nodes

Attributes and Metadata

Graph-Level Attributes

G.graph['name'] = 'Social Network'
G.graph['date'] = '2025-01-15'
print(G.graph)

Node Attributes

# Set at creation
G.add_node(1, time='5pm', weight=0.5)

# Set after creation
G.nodes[1]['time'] = '6pm'
nx.set_node_attributes(G, {1: 'red', 2: 'blue'}, 'color')

# Get attributes
G.nodes[1]
G.nodes[1]['time']
nx.get_node_attributes(G, 'color')

Edge Attributes

# Set at creation
G.add_edge(1, 2, weight=4.7, color='red')

# Set after creation
G[1][2]['weight'] = 5.0
nx.set_edge_attributes(G, {(1, 2): 10.5}, 'weight')

# Get attributes
G[1][2]
G[1][2]['weight']
G.edges[1, 2]
nx.get_edge_attributes(G, 'weight')

Subgraphs and Views

Subgraph Creation

# Create subgraph from node list
nodes_subset = [1, 2, 3, 4]
H = G.subgraph(nodes_subset)  # Returns view (references original)

# Create independent copy
H = G.subgraph(nodes_subset).copy()

# Edge-induced subgraph
edge_subset = [(1, 2), (2, 3)]
H = G.edge_subgraph(edge_subset)

Graph Views

# Reverse view (for directed graphs)
G_reversed = G.reverse()

# Convert between directed/undirected
G_undirected = G.to_undirected()
G_directed = G.to_directed()

Graph Information and Diagnostics

Basic Information

print(nx.info(G))   # Summary of graph structure

# Density (ratio of actual edges to possible edges)
nx.density(G)

# Check if graph is directed
G.is_directed()

# Check if graph is multigraph
G.is_multigraph()

Connectivity Checks

# For undirected graphs
nx.is_connected(G)
nx.number_connected_components(G)

# For directed graphs
nx.is_strongly_connected(G)
nx.is_weakly_connected(G)

Important Considerations

Floating Point Precision

Once graphs contain floating point numbers, all results are inherently approximate due to precision limitations. Small arithmetic errors can affect algorithm outcomes, particularly in minimum/maximum computations.

Memory Considerations

Each time a script starts, graph data must be loaded into memory. For large datasets, this can cause performance issues. Consider:

• Using efficient data formats (pickle for Python objects)
• Loading only necessary subgraphs
• Using graph databases for very large networks

Node and Edge Removal Behavior

When a node is removed, all edges incident with that node are automatically removed as well.