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New skill: social-graph-ranker - Weighted social graph traversal with exponential decay across hops - Bridge Score: B(m) = Σ w(t) · λ^(d(m,t)-1) ranks mutuals by target proximity - Extended Score incorporates 2nd-order network (mutual-of-mutual connections) - Final ranking includes engagement bonus for responsive connections - Runs in parallel with lead-intelligence skill for combined warm+cold outreach - Supports X API + LinkedIn CSV for graph harvesting - Outputs tiered action list: warm intros, direct outreach, network gap analysis Added to business-content install module. Catalog validates: 30/60/140.
200 lines
9.0 KiB
Markdown
200 lines
9.0 KiB
Markdown
---
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name: social-graph-ranker
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description: Weighted social graph traversal that ranks your network connections by proximity to target leads. Uses exponential decay across hops, parallel execution with lead-intelligence skill, and API-driven outreach prioritization. Replaces Apollo, Clay, and manual networking.
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metadata:
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tags: networking, outreach, leads, graph-theory, x-api, linkedin, exa
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---
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## When to Use
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Use this skill when you need to:
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- Find warm intro paths to specific people or companies
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- Rank your existing connections by networking value
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- Identify which mutuals to ask for introductions
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- Prioritize outbound outreach by warmth and proximity
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- Map your social graph against a target lead list
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## How It Works
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### Architecture
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Two parallel pipelines feed a unified ranking engine:
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```
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┌─────────────────────────────────────────────────────────┐
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│ SOCIAL GRAPH RANKER │
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├──────────────────────┬──────────────────────────────────┤
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│ INBOUND PIPELINE │ OUTBOUND PIPELINE │
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│ │ │
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│ Your Connections │ Target Lead List (ICP) │
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│ ┌──────────────┐ │ ┌──────────────────┐ │
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│ │ X Mutuals │ │ │ lead-intelligence │ │
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│ │ X Followers │ │ │ skill (parallel) │ │
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│ │ LI Connections│ │ │ Exa + X API + │ │
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│ └──────┬───────┘ │ │ enrichment agents │ │
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│ │ │ └────────┬─────────┘ │
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│ ▼ │ ▼ │
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│ ┌──────────────┐ │ ┌──────────────────┐ │
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│ │ Connection │ │ │ Ranked Lead List │ │
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│ │ Graph Build │ │ │ (scored by ICP │ │
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│ │ (adjacency) │ │ │ fit + response │ │
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│ └──────┬───────┘ │ │ probability) │ │
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│ │ │ └────────┬─────────┘ │
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│ └────────────┼──────────────┘ │
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│ ▼ │
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│ ┌──────────────────────┐ │
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│ │ GRAPH INTERSECTION │ │
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│ │ Match connections │ │
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│ │ against targets │ │
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│ └──────────┬───────────┘ │
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│ ▼ │
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│ ┌──────────────────────┐ │
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│ │ WEIGHTED RANKING │ │
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│ │ Exponential decay │ │
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│ │ across hops │ │
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│ └──────────┬───────────┘ │
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│ ▼ │
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│ ┌──────────────────────┐ │
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│ │ PRIORITIZED OUTPUT │ │
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│ │ 1. Warm intro asks │ │
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│ │ 2. Direct outreach │ │
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│ │ 3. Network gaps │ │
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│ └──────────────────────┘ │
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└─────────────────────────────────────────────────────────┘
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```
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### The Math: Weighted Graph Proximity Score
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Given:
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- **T** = set of target leads you want to reach
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- **M** = set of your mutuals/connections
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- **G** = social graph (adjacency)
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- **d(m, t)** = shortest path distance from mutual m to target t
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For each mutual m, compute:
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**Bridge Score:**
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```
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B(m) = Σ_{t ∈ T} w(t) · λ^{d(m,t) - 1}
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```
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Where:
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- `w(t)` = target weight (from lead-intelligence signal score: role 30%, industry 25%, activity 20%, influence 10%, location 10%, engagement 5%)
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- `λ` = decay factor, typically 0.5 (halves value each hop)
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- `d(m,t)` = hop distance (1 = direct connection, 2 = mutual-of-mutual, etc.)
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- Convention: `d(m,t) = 1` for direct connection, so `λ^0 = 1` (full value)
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**Properties:**
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- Direct connection to target: contributes `w(t) · 1.0`
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- One hop away: contributes `w(t) · 0.5`
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- Two hops: contributes `w(t) · 0.25`
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- Three hops: contributes `w(t) · 0.125`
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- Effectively zero beyond ~6 hops (Gaussian/exponential decay → 0)
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**Extended Score (second-order network value):**
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For deeper traversal, also consider the mutual's own network reach:
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```
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B_ext(m) = B(m) + α · Σ_{m' ∈ N(m) \ M} Σ_{t ∈ T} w(t) · λ^{d(m',t)}
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```
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Where:
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- `N(m) \ M` = connections of m that you DON'T already have
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- `α` = second-order discount (typically 0.3)
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- This captures: "even if m doesn't know my targets directly, m knows people I don't, who might"
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**Final Ranking:**
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```
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R(m) = B_ext(m) · (1 + β · engagement(m))
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```
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Where:
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- `engagement(m)` = normalized score of how responsive m is (reply rate, interaction frequency)
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- `β` = engagement bonus weight (typically 0.2)
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### Execution Steps
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1. **Build Target List**
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- Run lead-intelligence skill in parallel to generate scored ICP leads
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- Or provide manual target list with names/handles
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2. **Harvest Your Graph**
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- X API: `GET /2/users/:id/following` and `GET /2/users/:id/followers`
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- LinkedIn: connection export CSV or browser-use scraping
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- Build adjacency map: `mutual → [their connections]`
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3. **Intersect and Score**
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- For each mutual, check which targets they follow/connect with
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- Compute B(m) with decay
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- For top-k mutuals, expand one more hop and compute B_ext(m)
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4. **Generate Output**
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- Tier 1: Mutuals with B(m) > threshold → warm intro requests
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- Tier 2: Targets with no warm path → direct cold outreach via lead-intelligence
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- Tier 3: Network gaps → suggest who to follow/connect with to build bridges
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5. **Draft Messages**
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- Warm intro: "Hey [mutual], I saw you're connected to [target]. I'm working on [context]. Would you be open to making an intro?"
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- Uses outreach-drafter agent from lead-intelligence for personalization
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### Configuration
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```yaml
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# Target definition
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targets:
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- handle: "@targetperson"
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platform: x
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weight: 0.9 # override signal score
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# Decay parameters
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decay_factor: 0.5 # λ — halve value per hop
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max_depth: 3 # don't traverse beyond 3 hops
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second_order_discount: 0.3 # α — discount for network-of-network
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engagement_bonus: 0.2 # β — bonus for responsive mutuals
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# API configuration
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x_api:
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bearer_token: $X_BEARER_TOKEN
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rate_limit_delay: 1.1 # seconds between API calls
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linkedin:
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method: csv_export # or browser_use
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csv_path: ~/Downloads/Connections.csv
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```
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### Integration with lead-intelligence
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This skill runs IN PARALLEL with lead-intelligence:
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- lead-intelligence generates the target list (T) with signal scores
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- social-graph-ranker maps your network against those targets
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- Combined output: prioritized outreach plan with warm paths where available
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### Example Output
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```
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BRIDGE RANKING — Top 10 Mutuals by Network Value
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═══════════════════════════════════════════════════
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#1 @alex_quant (B=4.72)
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Direct → @kalshi_ceo (w=0.9), @polymarket_shayne (w=0.85)
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1-hop → @a16z_crypto (w=0.7, via @defi_mike)
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Action: Ask for intros to Kalshi + Polymarket
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#2 @sarah_vc (B=3.15)
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Direct → @sequoia_partner (w=0.95)
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1-hop → @yc_gustaf (w=0.8, via @batch_founder)
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Action: Ask for Sequoia intro
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#3 @dev_community (B=2.88)
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Direct → @cursor_ceo (w=0.6), @vercel_guillermo (w=0.6)
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2-hop → @anthropic_dario (w=0.95, via @cursor_ceo → @anthropic_team)
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Action: Ask for Cursor intro, mention Anthropic angle
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NETWORK GAPS — No warm path exists
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═══════════════════════════════════
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@target_x — Suggest following @bridge_person_1, @bridge_person_2
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@target_y — Direct cold outreach recommended (lead-intelligence draft ready)
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```
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