The nodes are tickers. The edges begin as correlations of historical price movements, normalized into positive affinity weights. I then apply Marchenko–Pastur-style filtering and Laplacian spectral coarse-graining, so the later graph is not a raw correlation graph. Its edges represent effective relationships that remain after filtering noise and viewing the network at a broader structural scale. Part of the goal is to break the strong symmetry of the near-complete correlation graph while preserving the topology implied by renormalization.
More broadly, I am trying to recover geometric properties embedded in market dynamics: geodesics, curvature, connectivity, transport paths, spectral structure, and eventually topological features such as cycles and cohomology. I am also interested in deriving useful physical analogues, such as susceptibility to shocks, diffusion and damping of stress, conductance or resistance across sectors, relaxation times, and critical transitions. The hope is to understand how the market responds to the uncomputable jazz band of human trading behavior by identifying relatively stable structures, analogous to Lagrange points and attractors.
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