social-graph-ranker

When to Use

Use this skill when you need to:

Find warm intro paths to specific people or companies
Rank your existing connections by networking value
Identify which mutuals to ask for introductions
Prioritize outbound outreach by warmth and proximity
Map your social graph against a target lead list

How It Works

Architecture

Two parallel pipelines feed a unified ranking engine:

┌─────────────────────────────────────────────────────────┐
│                    SOCIAL GRAPH RANKER                   │
├──────────────────────┬──────────────────────────────────┤
│   INBOUND PIPELINE   │        OUTBOUND PIPELINE         │
│                      │                                   │
│  Your Connections    │     Target Lead List (ICP)        │
│  ┌──────────────┐    │     ┌──────────────────┐         │
│  │ X Mutuals    │    │     │ lead-intelligence │         │
│  │ X Followers  │    │     │ skill (parallel)  │         │
│  │ LI Connections│   │     │ Exa + X API +     │         │
│  └──────┬───────┘    │     │ enrichment agents │         │
│         │            │     └────────┬─────────┘         │
│         ▼            │              ▼                    │
│  ┌──────────────┐    │     ┌──────────────────┐         │
│  │ Connection   │    │     │ Ranked Lead List  │         │
│  │ Graph Build  │    │     │ (scored by ICP    │         │
│  │ (adjacency)  │    │     │  fit + response   │         │
│  └──────┬───────┘    │     │  probability)     │         │
│         │            │     └────────┬─────────┘         │
│         └────────────┼──────────────┘                    │
│                      ▼                                   │
│         ┌──────────────────────┐                        │
│         │  GRAPH INTERSECTION  │                        │
│         │  Match connections   │                        │
│         │  against targets     │                        │
│         └──────────┬───────────┘                        │
│                    ▼                                     │
│         ┌──────────────────────┐                        │
│         │  WEIGHTED RANKING    │                        │
│         │  Exponential decay   │                        │
│         │  across hops         │                        │
│         └──────────┬───────────┘                        │
│                    ▼                                     │
│         ┌──────────────────────┐                        │
│         │  PRIORITIZED OUTPUT  │                        │
│         │  1. Warm intro asks  │                        │
│         │  2. Direct outreach  │                        │
│         │  3. Network gaps     │                        │
│         └──────────────────────┘                        │
└─────────────────────────────────────────────────────────┘

The Math: Weighted Graph Proximity Score

Given:

T = set of target leads you want to reach
M = set of your mutuals/connections
G = social graph (adjacency)
d(m, t) = shortest path distance from mutual m to target t

For each mutual m, compute:

Bridge Score:

B(m) = Σ_{t ∈ T} w(t) · λ^{d(m,t) - 1}

Where:

```
w(t)
```
= target weight (from lead-intelligence signal score: role 30%, industry 25%, activity 20%, influence 10%, location 10%, engagement 5%)
```
λ
```
= decay factor, typically 0.5 (halves value each hop)
```
d(m,t)
```
= hop distance (1 = direct connection, 2 = mutual-of-mutual, etc.)
Convention:
```
d(m,t) = 1
```
for direct connection, so
```
λ^0 = 1
```
(full value)

Properties:

Direct connection to target: contributes
```
w(t) · 1.0
```
One hop away: contributes
```
w(t) · 0.5
```
Two hops: contributes
```
w(t) · 0.25
```
Three hops: contributes
```
w(t) · 0.125
```
Effectively zero beyond ~6 hops (Gaussian/exponential decay → 0)

Extended Score (second-order network value):

For deeper traversal, also consider the mutual's own network reach:

B_ext(m) = B(m) + α · Σ_{m' ∈ N(m) \ M} Σ_{t ∈ T} w(t) · λ^{d(m',t)}

Where:

```
N(m) \ M
```
= connections of m that you DON'T already have
```
α
```
= second-order discount (typically 0.3)
This captures: "even if m doesn't know my targets directly, m knows people I don't, who might"

Final Ranking:

R(m) = B_ext(m) · (1 + β · engagement(m))

Where:

```
engagement(m)
```
= normalized score of how responsive m is (reply rate, interaction frequency)
```
β
```
= engagement bonus weight (typically 0.2)

Execution Steps

Build Target List
- Run lead-intelligence skill in parallel to generate scored ICP leads
- Or provide manual target list with names/handles
Harvest Your Graph
- X API:
```
GET /2/users/:id/following
```
  and
```
GET /2/users/:id/followers
```
- LinkedIn: connection export CSV or browser-use scraping
- Build adjacency map:
```
mutual → [their connections]
```
Intersect and Score
- For each mutual, check which targets they follow/connect with
- Compute B(m) with decay
- For top-k mutuals, expand one more hop and compute B_ext(m)
Generate Output
- Tier 1: Mutuals with B(m) > threshold → warm intro requests
- Tier 2: Targets with no warm path → direct cold outreach via lead-intelligence
- Tier 3: Network gaps → suggest who to follow/connect with to build bridges
Draft Messages
- Warm intro: "Hey [mutual], I saw you're connected to [target]. I'm working on [context]. Would you be open to making an intro?"
- Uses outreach-drafter agent from lead-intelligence for personalization

Configuration

yaml

# Target definition
targets:
  - handle: "@targetperson"
    platform: x
    weight: 0.9  # override signal score

# Decay parameters
decay_factor: 0.5        # λ — halve value per hop
max_depth: 3             # don't traverse beyond 3 hops
second_order_discount: 0.3  # α — discount for network-of-network
engagement_bonus: 0.2    # β — bonus for responsive mutuals

# API configuration
x_api:
  bearer_token: $X_BEARER_TOKEN
  rate_limit_delay: 1.1  # seconds between API calls
linkedin:
  method: csv_export     # or browser_use
  csv_path: ~/Downloads/Connections.csv

Integration with lead-intelligence

This skill runs IN PARALLEL with lead-intelligence:

lead-intelligence generates the target list (T) with signal scores
social-graph-ranker maps your network against those targets
Combined output: prioritized outreach plan with warm paths where available

Example Output

BRIDGE RANKING — Top 10 Mutuals by Network Value
═══════════════════════════════════════════════════

#1  @alex_quant (B=4.72)
    Direct → @kalshi_ceo (w=0.9), @polymarket_shayne (w=0.85)
    1-hop  → @a16z_crypto (w=0.7, via @defi_mike)
    Action: Ask for intros to Kalshi + Polymarket

#2  @sarah_vc (B=3.15)
    Direct → @sequoia_partner (w=0.95)
    1-hop  → @yc_gustaf (w=0.8, via @batch_founder)
    Action: Ask for Sequoia intro

#3  @dev_community (B=2.88)
    Direct → @cursor_ceo (w=0.6), @vercel_guillermo (w=0.6)
    2-hop  → @anthropic_dario (w=0.95, via @cursor_ceo → @anthropic_team)
    Action: Ask for Cursor intro, mention Anthropic angle

NETWORK GAPS — No warm path exists
═══════════════════════════════════
@target_x — Suggest following @bridge_person_1, @bridge_person_2
@target_y — Direct cold outreach recommended (lead-intelligence draft ready)

social-graph-ranker

NPX Install

Tags

SKILL.md Content

When to Use

How It Works

Architecture

The Math: Weighted Graph Proximity Score

Execution Steps

Configuration

Integration with lead-intelligence

Example Output