the mathematical study of graphs: vertices, edges, and their relationships
the cybergraph is a directed authenticated multigraph. particles are vertices, cyberlinks are directed edges, and neurons sign each edge with cryptographic authority
core results that underpin cyber:
Perron-Frobenius theorem — guarantees unique focus distribution for irreducible graphs
spectral gap — controls convergence speed of diffusion on the cybergraph
random walks — the probabilistic model behind cyberank and focus propagation
graph Laplacian — the operator driving springs and heat kernels in the tri-kernel
graph-theoretic measures in practice:
degree distribution reveals hub structure among particles
connected components identify isolated knowledge clusters
shortest paths define semantic distance between concepts
the cybergraph grows with every block. its topology encodes the collective intelligence of all neurons. graph theory provides the language to read that topology
see cybergraph, Perron-Frobenius theorem, diffusion, tri-kernel, cyberlinks