# Structural Metric Decisions

## Included in MVP

- direct dependencies: graph out-degree
- direct dependents: graph in-degree
- blast radius: reverse-graph reachability excluding the package itself
- PageRank: defined in `pagerank.md`
- SCC: Kosaraju or Tarjan over the directed graph
- weak components: connected components after ignoring direction
- concentration: direct-edge shares, in-degree Gini and HHI, and union coverage
  of the top blast-radius packages

For in-degree values `x_i`, Gini is computed from the sorted values using the
standard discrete formula. HHI is `sum(s_i^2)` where `s_i = x_i / sum(x)`.
Here HHI describes concentration of dependency edges, not market power.

## Investigated but excluded from the initial ranking surface

The undirected projection contains 154 articulation points and 486 bridge
edges. The graph is sparse, and many reported bridges are simply the only edge
to a leaf package. Discarding dependency direction also makes “bottleneck” easy
to overstate. These values may be exposed as an advanced diagnostic with local
neighborhood evidence, but are not an MVP headline ranking.

Exact betweenness centrality is also excluded initially. It is computable at
this scale, but its path-count interpretation overlaps with the noisy
undirected cut structure and needs a stronger user question before becoming a
product metric.

Dominators are excluded because the ecosystem graph has no canonical root.
Choosing an artificial super-root would create a mathematically valid result
with weak package-ecosystem meaning.