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:

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:

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:

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

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

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