Social graph ranker

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:

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