Count paths of three or more hops from node degrees #135

Problem

The two-hop count rewrite counts MATCH (a)-[:R]->(b)-[:S]->(c) RETURN count(*) as Σ_b n1(b) × n2(b), the product of each middle node's neighbours on either side, without building any path. A longer pattern, such as (a)-[:R]->(b)-[:S]->(c)-[:T]->(d) RETURN count(*), keeps the join plan and builds every path before counting it.

The first-hop count from #113 collapses only the first hop of a longer pattern; the hops after it still emit one row per match. Variable-length hops (-[:R*2..3]->) are never counted from degrees.

Idea

Count each end hop per node in place and sum their products over the middle hop's edges: Σ_(b,c) in(b) × out(c) for three hops, which follows the edges rather than the paths. Longer fixed-length patterns chain the same per-node sums.

Two things limit it:

• Same-type hops. Cypher's rule that a path uses each edge once can exclude pairs of hops that aren't adjacent, such as r1 = r3 on a two-cycle, so the correction goes beyond the self-loop and shared-end cases the two-hop count handles. A first version could apply only when no two hops share a type.
• Variable-length hops. The rule applies across the whole path, so degree products overcount any path that would revisit an edge. Short bounded lengths may be countable with corrections; otherwise they keep the current plan.

Split from #78.