Weighted social-graph ranking for warm intro discovery, bridge scoring, and network gap analysis across X and LinkedIn. Use when the user wants the reusable…
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 pathsdon't have the plugin yet? install it then click "run inline in claude" again.