Formula
x = (I - α A)^(-1) · 1. Where α < 1/λ₁ ensures convergence. Sum over k of (α A)^k · 1.
Advertisement
Interpretation
x_v = sum over k of (α^k) · (# paths of length k ending at v). Longer paths contribute less.
Advertisement
vs Eigenvector
Eigenvector centrality: limit case (single largest eigenvalue). Katz includes contributions from smaller eigenvalues.
Iterative computation
x_new = 1 + α A x_old. Converge in log(1/ε)/log(1/(α·λ₁)) iterations.