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

• Build the weighted target set.

• Pull the user's graph from X, LinkedIn, or both.

• Compute direct bridge scores.

• Expand second-order candidates for the highest-value mutuals.

• Rank by R(m).

• 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