Social Graph Ranker

---
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.
metadata:
  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: