Graph Theory Deep Dive: The Logic of Connection

Graph theory is the mathematical study of networks. In the context of Wikantik, it provides the formal framework for both the Page Graph (links) and the Knowledge Graph (entities).

1. Spectral Graph Theory

Spectral graph theory studies the properties of a graph in relation to the characteristic polynomial, eigenvalues, and eigenvectors of its matrices (such as the adjacency matrix or Laplacian matrix).

• Connectivity: The second smallest eigenvalue of the Laplacian (\lambda_2) is a measure of how well-connected the graph is (algebraic connectivity).
• Partitioning: Eigenvectors are used in spectral clustering to identify semantic "islands" in large datasets.

2. Network Flow and Centrality

• Max-Flow Min-Cut: A fundamental theorem used in logistics and routing.
• Centrality Measures: Identifying influential nodes (hubs) using PageRank, Betweenness, and Eigenvector centrality.

For foundations, see Discrete Mathematics.