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Network Analysis (Centrality & Bottlenecks)

fastspa can treat extracted structural paths as a directed, weighted supply-chain network. This enables common network science workflows like bottleneck identification.

Build a path-induced network​

from fastspa import SPA

paths = SPA(A, emissions, sectors=sectors).analyze(sector=42, depth=8)

edges = paths.edge_weights()  # (downstream, upstream) -> weight

By default, each edge weight is the sum of the contributing path fractions that traverse that edge.

Betweenness centrality​

bc = paths.betweenness_centrality()

# Inspect the most central transmission sectors
bottlenecks = paths.bottleneck_sectors(top_n=10)

Topology summary​

topo = paths.network_topology()
print(topo["n_nodes"], topo["n_edges"], topo["density"])

Interpretation notes​

  • The graph is directed from the target sector (root) upstream to suppliers.
  • Centrality is computed over the path-induced subnetwork (not the full A-matrix).
  • For policy use, bottlenecks are typically the highest betweenness sectors (excluding the target).