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