Articles /Network Graph Analysis /Part 1
Foundations
Graph representations, key metrics, and visualization with NetworkX
Graph TheoryPythonNetworkXTutorial
Graphs are everywhere: social networks, transportation routes, biological pathways, the internet itself. A graph is simply a set of nodes connected by edges, yet this minimal structure encodes rich relational information that matrices and tables miss. This article lays the groundwork for a series on network graph analysis: starting with the representations, metrics, and visualizations you need to reason about any network.
The series draws on three portfolio projects that use graph techniques: Calendar Graph project ↗ (organizational network analysis), Graphception project ↗ (concept extraction and associative networks), and Books project ↗ (LLM-generated outlines as tree graphs).
What Is a Graph and Why It Matters
A graph G = (V, E) consists of a vertex set V and an edge set E. Edges can be directed or undirected, weighted or unweighted. This abstraction lets us model friendships, citations, dependencies, and countless other relationships in a single framework.
Representations: Adjacency Matrix, Edge List, Adjacency List
How you store a graph matters. An adjacency matrix is an n×n array where entry (i,j) indicates an edge between nodes i and j: great for dense graphs and linear algebra. An edge list is a simple collection of (u, v) pairs: compact and easy to stream. An adjacency list maps each node to its neighbors: ideal for sparse graphs and traversal algorithms. NetworkX abstracts over these, but understanding the tradeoffs guides performance decisions.
Key Metrics: Degree, Clustering, Path Length, Density
A handful of metrics capture a graph’s structure:
- Degree: how many connections a node has. The degree distribution often reveals whether a network is random, scale-free, or something else.
- Clustering coefficient: the fraction of a node’s neighbors that are also connected to each other. High clustering suggests tight-knit communities.
- Average shortest path length: the typical number of hops between any two nodes. Small-world networks have short paths despite high clustering.
- Density: the ratio of actual edges to possible edges. Most real-world networks are sparse.
Visualization Approaches
Layout algorithms turn abstract graphs into spatial pictures:
- Force-directed (spring): treats edges as springs and nodes as repelling charges. Good for revealing clusters.
- Hierarchical: arranges nodes in layers. Suited for DAGs and tree-like structures.
- Circular: places nodes on a ring. Useful for comparing connectivity patterns.
No layout is objectively best: each reveals different aspects of the same graph.
Series Roadmap
With these foundations in place, the series branches into three directions:
Branch A: Social & Organizational Networks
- Part 2: Community Detection in Social Graphs: modularity, Louvain, stochastic block models
- Part 3: Centrality, Influence, and Spectral Methods: degree, betweenness, PageRank, graph Laplacian
Branch B: Knowledge Graphs
- Part 4: Building Knowledge Graphs from Text: entity extraction, co-occurrence and semantic graphs
- Part 5: LLM-Augmented Knowledge Graphs: LLM extraction, outline-to-tree, hybrid construction
- Part 6: GraphRAG: graph-based retrieval, community summaries, geopolitical world graphs
Branch C: Graph Deep Learning
- Part 7: Graph Neural Networks: GCN, GAT, message passing
- Part 8: Temporal Graph Networks: dynamic graphs, temporal attention, evolving metrics
- Part 9: Causal and Bayesian Graph Networks: DAGs, do-calculus, probabilistic inference
Each branch builds on the representations and metrics introduced here.
Degree distributions and clustering coefficients describe a graph's texture -- but the most useful structure is often hidden in densely connected subgroups.