refactor: extract social graph ranking core

skills/social-graph-ranker/SKILL.md

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+---
+name: social-graph-ranker
+description: Weighted social-graph ranking for warm intro discovery, bridge scoring, and network gap analysis across X and LinkedIn. Use when the user wants the reusable graph-ranking engine itself, not the broader outreach or network-maintenance workflow layered on top of it.
+origin: ECC
+---
+
+# Social Graph Ranker
+
+Canonical weighted graph-ranking layer for network-aware outreach.
+
+Use this when the user needs to:
+
+- rank existing mutuals or connections by intro value
+- map warm paths to a target list
+- measure bridge value across first- and second-order connections
+- decide which targets deserve warm intros versus direct cold outreach
+- understand the graph math independently from `lead-intelligence` or `connections-optimizer`
+
+## When To Use This Standalone
+
+Choose this skill when the user primarily wants the ranking engine:
+
+- "who in my network is best positioned to introduce me?"
+- "rank my mutuals by who can get me to these people"
+- "map my graph against this ICP"
+- "show me the bridge math"
+
+Do not use this by itself when the user really wants:
+
+- full lead generation and outbound sequencing -> use `lead-intelligence`
+- pruning, rebalancing, and growing the network -> use `connections-optimizer`
+
+## Inputs
+
+Collect or infer:
+
+- target people, companies, or ICP definition
+- the user's current graph on X, LinkedIn, or both
+- weighting priorities such as role, industry, geography, and responsiveness
+- traversal depth and decay tolerance
+
+## Core Model
+
+Given:
+
+- `T` = weighted target set
+- `M` = your current mutuals / direct connections
+- `d(m, t)` = shortest hop distance from mutual `m` to target `t`
+- `w(t)` = target weight from signal scoring
+
+Base bridge score:
+
+```text
+B(m) = Σ_{t ∈ T} w(t) · λ^(d(m,t) - 1)
+```
+
+Where:
+
+- `λ` is the decay factor, usually `0.5`
+- a direct path contributes full value
+- each extra hop halves the contribution
+
+Second-order expansion:
+
+```text
+B_ext(m) = B(m) + α · Σ_{m' ∈ N(m) \\ M} Σ_{t ∈ T} w(t) · λ^(d(m',t))
+```
+
+Where:
+
+- `N(m) \\ M` is the set of people the mutual knows that you do not
+- `α` discounts second-order reach, usually `0.3`
+
+Response-adjusted final ranking:
+
+```text
+R(m) = B_ext(m) · (1 + β · engagement(m))
+```
+
+Where:
+
+- `engagement(m)` is normalized responsiveness or relationship strength
+- `β` is the engagement bonus, usually `0.2`
+
+Interpretation:
+
+- Tier 1: high `R(m)` and direct bridge paths -> warm intro asks
+- Tier 2: medium `R(m)` and one-hop bridge paths -> conditional intro asks
+- Tier 3: low `R(m)` or no viable bridge -> direct outreach or follow-gap fill
+
+## Scoring Signals
+
+Weight targets before graph traversal with whatever matters for the current priority set:
+
+- role or title alignment
+- company or industry fit
+- current activity and recency
+- geographic relevance
+- influence or reach
+- likelihood of response
+
+Weight mutuals after traversal with:
+
+- number of weighted paths into the target set
+- directness of those paths
+- responsiveness or prior interaction history
+- contextual fit for making the intro
+
+## Workflow
+
+1. Build the weighted target set.
+2. Pull the user's graph from X, LinkedIn, or both.
+3. Compute direct bridge scores.
+4. Expand second-order candidates for the highest-value mutuals.
+5. Rank by `R(m)`.
+6. Return:
+   - best warm intro asks
+   - conditional bridge paths
+   - graph gaps where no warm path exists
+
+## Output Shape
+
+```text
+SOCIAL GRAPH RANKING
+====================
+
+Priority Set:
+Platforms:
+Decay Model:
+
+Top Bridges
+- mutual / connection
+  base_score:
+  extended_score:
+  best_targets:
+  path_summary:
+  recommended_action:
+
+Conditional Paths
+- mutual / connection
+  reason:
+  extra hop cost:
+
+No Warm Path
+- target
+  recommendation: direct outreach / fill graph gap
+```
+
+## Related Skills
+
+- `lead-intelligence` uses this ranking model inside the broader target-discovery and outreach pipeline
+- `connections-optimizer` uses the same bridge logic when deciding who to keep, prune, or add
+- `brand-voice` should run before drafting any intro request or direct outreach
+- `x-api` provides X graph access and optional execution paths