networkx-graph-analysis

NetworkX Graph Analysis

Overview

NetworkX is a Python library for creating, manipulating, and analyzing complex networks and graphs. It provides data structures for undirected, directed, and multi-edge graphs along with a comprehensive collection of graph algorithms, generators, and I/O utilities. Use NetworkX when working with relationship data in social networks, biological interaction networks, transportation systems, citation graphs, or any domain involving pairwise entity relationships.

When to Use

• Analyzing protein-protein interaction networks, gene regulatory networks, or metabolic pathways
• Computing centrality measures (degree, betweenness, PageRank) to identify important nodes
• Finding shortest paths or optimal routes in transportation or communication networks
• Detecting communities or clusters in social networks or co-expression data
• Generating synthetic networks (scale-free, small-world, random) for simulation or null models
• Reading and writing graph data in standard formats (GraphML, GML, edge lists, JSON)
• Visualizing network topology with node/edge attribute mapping
• Checking graph properties: connectivity, planarity, isomorphism, DAG structure
• For large-scale graphs (100K+ nodes) where speed is critical, use igraph or graph-tool instead
• For billion-edge graphs or GPU-accelerated analytics, use graph-tool with OpenMP or cuGraph
• For graph neural networks and deep learning on graphs, use torch-geometric-graph-neural-networks

Prerequisites

• Python packages: networkx, matplotlib, scipy, pandas, numpy
• Optional: pydot or pygraphviz (Graphviz layouts)

pip install networkx matplotlib scipy pandas numpy

Quick Start

import networkx as nx

# Create a graph and add edges with weights
G = nx.karate_club_graph()
print(f"Nodes: {G.number_of_nodes()}, Edges: {G.number_of_edges()}")
# Nodes: 34, Edges: 78

# Compute centrality and find most central node
bc = nx.betweenness_centrality(G)
top_node = max(bc, key=bc.get)
print(f"Most central node: {top_node}, betweenness: {bc[top_node]:.3f}")

# Detect communities
from networkx.algorithms import community
comms = community.greedy_modularity_communities(G)
print(f"Communities found: {len(comms)}")

Core API

Module 1: Graph Creation and Types

import networkx as nx

# Undirected graph (most common)
G = nx.Graph()
G.add_node("protein_A", type="kinase", weight=1.5)
G.add_nodes_from(["protein_B", "protein_C"])
G.add_edge("protein_A", "protein_B", weight=0.9, interaction="phosphorylation")
G.add_edges_from([("protein_B", "protein_C"), ("protein_A", "protein_C")])
print(f"Nodes: {G.number_of_nodes()}, Edges: {G.number_of_edges()}")
# Nodes: 3, Edges: 3

# Directed graph (gene regulation, citations)
D = nx.DiGraph()
D.add_edges_from([("TF1", "geneA"), ("TF1", "geneB"), ("TF2", "geneA")])
print(f"TF1 out-degree: {D.out_degree('TF1')}")  # 2

# MultiGraph (multiple relationship types between same nodes)
M = nx.MultiGraph()
M.add_edge("A", "B", key="binding", affinity=0.8)
M.add_edge("A", "B", key="regulation", effect="inhibition")
print(f"Edges between A-B: {M.number_of_edges('A', 'B')}")  # 2

Module 2: Node and Edge Operations

import networkx as nx
G = nx.karate_club_graph()

# Query structure
print(f"Degree of node 0: {G.degree(0)}")
print(f"Neighbors of node 0: {list(G.neighbors(0))[:5]}")
print(f"Has edge 0-1: {G.has_edge(0, 1)}")

# Set and get attributes
G.nodes[0]["role"] = "instructor"
nx.set_node_attributes(G, {0: "high", 33: "high"}, "importance")
G[0][1]["weight"] = 0.95

# Iterate with data
for u, v, data in G.edges(data=True):
    if "weight" in data:
        print(f"  Edge {u}-{v}: weight={data['weight']}")
        break

# Subgraphs (returns read-only view; use .copy() for mutable)
H = G.subgraph([0, 1, 2, 3, 4, 5]).copy()
print(f"Subgraph: {H.number_of_nodes()} nodes, {H.number_of_edges()} edges")

Module 3: Graph Analysis (Centrality)

import networkx as nx
G = nx.karate_club_graph()

degree_c = nx.degree_centrality(G)
between_c = nx.betweenness_centrality(G, weight="weight")
# For large graphs, approximate: nx.betweenness_centrality(G, k=100)
close_c = nx.closeness_centrality(G)
eigen_c = nx.eigenvector_centrality(G, max_iter=1000)
pr = nx.pagerank(G, alpha=0.85)

# Compare top nodes across measures
for name, metric in [("Degree", degree_c), ("Betweenness", between_c),
                     ("Closeness", close_c), ("PageRank", pr)]:
    top = max(metric, key=metric.get)
    print(f"{name:12s}: top node={top}, score={metric[top]:.4f}")

Module 4: Path and Connectivity

import networkx as nx
G = nx.karate_club_graph()

# Shortest path
path = nx.shortest_path(G, source=0, target=33)
length = nx.shortest_path_length(G, source=0, target=33)
print(f"Shortest path 0->33: {path} (length {length})")
print(f"Average shortest path length: {nx.average_shortest_path_length(G):.3f}")

# Connected components
print(f"Connected: {nx.is_connected(G)}")
components = list(nx.connected_components(G))
print(f"Components: {len(components)}, largest: {len(max(components, key=len))}")

# For directed graphs: strong/weak connectivity
D = nx.DiGraph([(0,1),(1,2),(2,0),(3,4)])
print(f"Strongly connected: {list(nx.strongly_connected_components(D))}")

# Connectivity measures
print(f"Node connectivity: {nx.node_connectivity(G)}")
print(f"Edge connectivity: {nx.edge_connectivity(G)}")

Module 5: Community Detection

Partition networks into densely connected groups.

import networkx as nx
from networkx.algorithms import community
import itertools

G = nx.karate_club_graph()

# Greedy modularity maximization
comms_greedy = community.greedy_modularity_communities(G)
mod_score = community.modularity(G, comms_greedy)
print(f"Greedy: {len(comms_greedy)} communities, modularity={mod_score:.4f}")

# Label propagation (fast, non-deterministic)
comms_lpa = community.label_propagation_communities(G)
print(f"Label propagation: {len(list(comms_lpa))} communities")

# Girvan-Newman (hierarchical, edge betweenness removal)
gn = community.girvan_newman(G)
# Get first level of partition
first_level = next(gn)
print(f"Girvan-Newman first split: {len(first_level)} groups")
print(f"  Sizes: {[len(c) for c in first_level]}")

Module 6: I/O and Serialization

import networkx as nx
import pandas as pd
import json

G = nx.karate_club_graph()

# Edge list (simple text format)
nx.write_edgelist(G, "karate.edgelist")
G_loaded = nx.read_edgelist("karate.edgelist", nodetype=int)

# GraphML (preserves all attributes, XML-based)
nx.write_graphml(G, "karate.graphml")
G_xml = nx.read_graphml("karate.graphml")

# JSON (node-link format, web-friendly for d3.js)
data = nx.node_link_data(G)
with open("karate.json", "w") as f:
    json.dump(data, f)

# Pandas integration
df = pd.DataFrame({"source": [1,2,3], "target": [2,3,4], "weight": [0.5,1.0,0.75]})
G_pd = nx.from_pandas_edgelist(df, "source", "target", edge_attr="weight")
df_out = nx.to_pandas_edgelist(G_pd)
print(f"Pandas round-trip: {len(df_out)} edges")

# NumPy/SciPy matrices
A = nx.to_numpy_array(G)
print(f"Adjacency matrix shape: {A.shape}")
A_sparse = nx.to_scipy_sparse_array(G, format="csr")  # Memory-efficient

Module 7: Visualization

import networkx as nx
import matplotlib.pyplot as plt

G = nx.karate_club_graph()
pos = nx.spring_layout(G, seed=42)

# Color by degree, size by betweenness centrality
bc = nx.betweenness_centrality(G)
fig, ax = plt.subplots(figsize=(10, 8))
nx.draw(G, pos=pos, ax=ax,
        node_color=[G.degree(n) for n in G.nodes()], cmap=plt.cm.viridis,
        node_size=[3000 * bc[n] + 100 for n in G.nodes()],
        edge_color="gray", alpha=0.8, with_labels=True, font_size=8)
plt.tight_layout()
plt.savefig("network.png", dpi=300, bbox_inches="tight")
plt.savefig("network.pdf", bbox_inches="tight")  # Vector format
print("Saved network.png and network.pdf