social-graph-ranker
用加權圖譜算橋接分數，找出最適合替你引薦的人脈
中文翻譯
---
name: social-graph-ranker
description: 用加權社交圖譜排名，找出 warm intro 管道、計算橋接分數，並分析 X 和 LinkedIn 上的人脈缺口。使用者要的是可重複使用的圖譜排名引擎本身，而不是疊在它上面的完整開發信或人脈維護流程時使用。
metadata:
origin: ECC
---
# Social Graph Ranker
用於人脈導向開發聯繫的標準加權圖譜排名層。
使用者需要做這些事時，就用這個：
- 依引薦價值為現有的共同好友或人脈排名
- 把通往目標清單的 warm 路徑畫出來
- 衡量一階和二階人脈的橋接價值
- 判斷哪些目標值得請人 warm intro，哪些該直接 cold outreach
- 想獨立於 `lead-intelligence` 或 `connections-optimizer` 之外，理解圖譜的數學
## 何時單獨使用
使用者主要想要排名引擎時，選這個 skill：
- 「我的人脈裡誰最適合替我引薦？」
- 「依誰能幫我連到這些人，替我的共同好友排名」
- 「把我的圖譜對照這個 ICP」
- 「讓我看橋接的數學」
使用者真正想要的是下面這些時，不要單獨用它：
- 完整的潛在客戶開發和外送序列 -> 用 `lead-intelligence`
- 修剪、重新平衡和擴展人脈 -> 用 `connections-optimizer`
## 輸入
蒐集或推斷：
- 目標人物、公司或 ICP 定義
- 使用者目前在 X、LinkedIn 或兩者上的圖譜
- 加權的優先項目，例如職務、產業、地區和回應度
- 走訪深度和衰減容忍度
## 核心模型
給定：
- `T` = 加權的目標集合
- `M` = 你目前的共同好友 / 直接人脈
- `d(m, t)` = 從共同好友 `m` 到目標 `t` 的最短跳數距離
- `w(t)` = 由訊號評分得到的目標權重
基本橋接分數：
```text
B(m) = Σ_{t ∈ T} w(t) · λ^(d(m,t) - 1)
```
其中：
- `λ` 是衰減係數，通常是 `0.5`
- 直接路徑貢獻完整價值
- 每多一跳，貢獻減半
二階擴展：
```text
B_ext(m) = B(m) + α · Σ_{m' ∈ N(m) \\ M} Σ_{t ∈ T} w(t) · λ^(d(m',t))
```
其中：
- `N(m) \\ M` 是這位共同好友認識、但你不認識的人的集合
- `α` 是二階觸及的折扣，通常是 `0.3`
依回應度調整的最終排名：
```text
R(m) = B_ext(m) · (1 + β · engagement(m))
```
其中：
- `engagement(m)` 是正規化後的回應度或關係強度
- `β` 是互動加成，通常是 `0.2`
解讀：
- 第 1 級：`R(m)` 高而且有直接橋接路徑 -> 請對方 warm intro
- 第 2 級：`R(m)` 中等而且有一跳的橋接路徑 -> 有條件的引薦請求
- 第 3 級：`R(m)` 低，或沒有可行的橋接 -> 直接聯繫，或補上圖譜缺口
## 評分訊號
走訪圖譜之前，用對當前優先項目重要的任何因素替目標加權：
- 職務或頭銜吻合度
- 公司或產業適配度
- 目前的活躍度和近期性
- 地理相關性
- 影響力或觸及範圍
- 回應的可能性
走訪之後，用這些替共同好友加權：
- 通往目標集合的加權路徑數量
- 這些路徑的直接程度
- 回應度或過去的互動歷史
- 幫忙引薦的情境適配度
## 工作流程
1. 建立加權的目標集合。
2. 從 X、LinkedIn 或兩者拉出使用者的圖譜。
3. 計算直接橋接分數。
4. 替價值最高的共同好友展開二階候選人。
5. 依 `R(m)` 排名。
6. 回傳：
- 最佳的 warm intro 請求
- 有條件的橋接路徑
- 沒有 warm 路徑的圖譜缺口
## 輸出格式
```text
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
```
## 相關 Skill
- `lead-intelligence` 在更廣的目標探索和開發聯繫 pipeline 裡使用這個排名模型
- `connections-optimizer` 在決定要保留、修剪或新增誰時，使用同樣的橋接邏輯
- 起草任何引薦請求或直接聯繫之前，應該先執行 `brand-voice`
- `x-api` 提供 X 圖譜的存取，以及選用的執行路徑英文原文
---
name: social-graph-ranker
description: 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 graph-ranking engine itself, not the broader outreach or network-maintenance workflow layered on top of it.
metadata:
origin: ECC
---
# 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:
```text
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:
```text
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:
```text
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
```text
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