Add Betweenness Centrality (Brandes's Algorithm) derivation and EDGE cascade

[jowens]

Summary

This PR adds the complete tensor algebraic derivation and Jekyll-formatted EDGE cascade page for Betweenness Centrality (Brandes's Algorithm) at _algorithms/betweenness-centrality.md.

Contents Included:

• Foundational Formulation: Derivation from the classical $O(|V|^3)$ 3-index tensor contraction $\mathcal{T}{s, v, t} = \frac{\sigma{st}(v)}{\sigma_{st}}$ to Brandes's $O(|V||E|)$ Two-Phase Forward-Backward Einsum Cascade over shortest-path DAGs.
• Concrete Working Traces:
  • 4-node diamond graph (fractional path counts $\sigma=2, \delta=0.5$)
  • 5-node bridge graph (bottleneck articulation)
• Formal EDGE Cascade Specification: Forward primal BFS discovery, backward adjoint reverse-topological sweep, and source reduction.
• 10 Problem Applications:
  • 4 previously derived/published variants (Girvan-Newman, Stress, Load, Bounded/Decay)
  • 6 opportunities for exploration in EDGE (Vitality, GNN Sensitivities, Streaming BC, Group BC, Pareto BC, Cascading Failures) with all verified [Wikipedia, DOI] citations.
• Algorithmic Suboptimality Analysis in Existing Software: Concrete analysis of bottlenecks and Brandes factorization remedies in NetworkX (closeness_vitality, group_betweenness_centrality, load_centrality), NetworKit (GroupBetweenness, DynBetweenness), and igraph (igraph_community_edge_betweenness).