foundations-network-science

Network Science Foundations

12 canonical network-science primitives, each solving a distinct structural or dynamic analysis problem. Primitives are domain-agnostic: the same PageRank that ranks web pages ranks citation authority, package influence, and audience amplification. The same percolation threshold that governs epidemic spread governs cascading failure in dependency graphs.

When to Apply

Apply network-science when:

• The data IS a graph — citations, dependencies, follower graphs, supply chains, knowledge graphs
• The system is a graph even if the data is not — LLM multi-agent communication topology, agent memory graphs, tool-call graphs (see Agent Topology as a Graph Problem)
• Spread/contagion question — viral coefficient, R₀, percolation threshold
• Centrality question — "which nodes are critical?" (PageRank, betweenness, eigenvector)
• Community detection — clustering nodes by structural similarity (Louvain, Leiden)
• Blast-radius / dependency-impact analysis on services or modules

Skip and use simpler alternatives when:

• Data is tabular and relationships aren't structural — standard analytics suffices
• Graph has < 50 nodes — visual inspection beats algorithmic centrality
• Question is about strategic interaction at the node level — use foundations-game-theory
• Question is about queue or flow through a single bottleneck — use foundations-queueing-theory or theory-of-constraints
• Edges are weak proxies (e.g. "users who viewed both products") — centrality is unreliable; validate edge semantics first
• "Network effects" is a marketing claim, not a measured viral coefficient — quantify R first or skip the analysis

The data is tabular but might still be a graph problem. Three criteria (Broadwater & Stillman 2025, §1.4) — any one is grounds to reframe: implicit relationships and interdependencies (entities connected by undocumented influence, co-investment, or co-occurrence rather than a recorded relation); high dimensionality and sparsity (many entities, few direct interactions — recommender interaction data, molecules; also the cold-start motivation); complex nonlocal interactions (an entity's outcome depends on entities reachable only through intermediaries — supply-chain cascades, propagation through a network over time). Key indicators and the closing self-test questions are in 10-graph-embeddings.md. If a criterion holds, design the structure explicitly with #12 before ingest, and establish a tabular (non-GNN) baseline before attributing anything to the graph.