Sociogram

Social network diagrams with mutual choices, rejections, group coloring, force-directed or hierarchical layout. Auto-detects sociometric roles — stars, isolates, cliques. Based on Moreno sociometry.

Moreno (1934) sociometry model + modern social network analysis conventions + 多领域应用扩展。群体内社会关系的可视化与分析。

Primary References:

Moreno, J.L. (1934). Who Shall Survive? Foundations of Sociometry, Group Psychotherapy and Sociodrama. Beacon House.

Moreno, J.L. & Jennings, H.H. (1938). Statistics of social configurations. Sociometry, 1(3/4), 342-374.

Brandes, U. et al. (2011). Effects of sociogram drawing conventions and edge crossings in social network visualization. J Graph Algorithms Appl. 15(1), 157-176.

Hanneman, R.A. & Riddle, M. (2005). Introduction to Social Network Methods. UC Riverside.

FBI Law Enforcement Bulletin (2014). Social Network Analysis: A Systematic Approach for Investigating.

1. What is a Sociogram?

Sociogram 是由 Jacob L. Moreno 于 1934 年开发的群体社会关系可视化工具。与 ecomap（个人↔外部系统）不同，sociogram 关注的是群体内部成员之间的关系网络——谁选择了谁、谁被孤立、谁是核心、哪些人形成了小圈子。

核心区别：

维度	Ecomap	Sociogram
焦点	一个人/家庭 vs 外部系统	群体内所有成员互相之间
布局	径向（中心-外围）	网络图（force-directed / circular）
连线含义	关系质量（强/弱/压力）	社会选择（选择/拒绝/相互）
用途	临床评估	群体动力学分析

2. Who Uses Sociograms — User Segments

2.1 Education（最大用户群）

教师 + 学校心理咨询师是 sociogram 的第一大用户群。典型场景：

场景	方法	目的
课堂社交评估	让每个学生列出 2 名想合作的同学	识别 stars（受欢迎）、isolates（被孤立）、cliques（小圈子）
座位/分组安排	基于 sociogram 数据优化	确保 isolates 被纳入、打破排他性 cliques
霸凌预防	定期 sociogram 追踪	发现关系变化、早期干预
夏令营/班级分配	师生关系映射	平衡组间社交动力

关键词信号： "sociogram classroom"、"sociogram maker"（教师工具意图）

社工 + 群体治疗师 + 心理剧治疗师：

场景	方法	目的
Group therapy 动力评估	治疗师观察 + 成员问卷	识别联盟、冲突、权力结构
Social atom（社会原子）	个人画出最重要的人际关系	Moreno 的核心技术，warm-up for psychodrama
家庭系统动力	家庭成员间的选择/排斥	补充 genogram 的动力维度
社区评估	机构间关系映射	识别服务gap、资源集中度

与 Schematex 现有用户的重叠： 使用 genogram + ecomap 的社工/治疗师也是 sociogram 的天然用户。

2.3 Organizational Development（企业用户）

HR 专家 + 组织发展顾问 + 团队 lead：

场景	方法	目的
非正式影响力映射	"你遇到问题会找谁帮忙？"	发现隐性领导者 vs 正式 org chart
团队组建	跨部门社交网络分析	优化跨职能团队组合
信息流分析	"你从谁那里获取工作信息？"	识别信息瓶颈和孤岛
合并后文化整合	两个团队的交叉连接	评估整合进度

2.4 Law Enforcement / Intelligence（高价值专业用户）

执法分析师 + 情报分析师：

场景	方法	目的
犯罪网络分析	电话记录、社交媒体、监控数据 → link analysis	识别组织核心人物、中间人、外围
帮派结构映射	逮捕记录、同车记录	理解帮派层级和领地
嫌疑人社交圈	1-2 度关系网络	追踪逃犯、预测行为
反恐网络分析	通讯模式 + 资金流	识别 cell 结构

注意： 执法场景通常使用 Palantir、i2 Analyst's Notebook 等专业工具，但基础的 sociogram 可视化能力（轻量、可嵌入、Text DSL 输入）是差异化机会。

2.5 Academic Research（长尾用户）

社会学、人类学、政治学研究中的社会网络分析。通常使用 Gephi、NetworkX、Pajek 等重型工具。Schematex 的机会在于轻量快速可视化——论文插图、教学演示。

3. Sociogram Structure

Sociogram 由三层组成：

节点 (Nodes) — 群体中的个体成员
连线 (Edges) — 成员之间的社会关系/选择
结构模式 (Patterns) — 从节点+连线中涌现的群体结构

4. Node Types & Symbols

4.1 Standard Node Shape

Element	Shape	SVG	含义
Default member	Circle (r=20)	`<circle>`	群体中的个体
Star (popular)	Circle + star marker	`<circle>` + `<polygon>` overlay	被多人选择的核心人物
Isolate	Circle + dashed border	`<circle stroke-dasharray>`	无人选择/未选择他人
Ego (focal person)	Double circle (concentric)	两个 `<circle>`，gap=3px	分析的焦点人物（egocentric 视图）

Auto-detection rules（基于数据自动标记）：

Star: in-degree ≥ mean + 1.5 × SD，或 in-degree ≥ group_size × 0.4
Isolate: in-degree = 0 AND out-degree = 0
Neglectee: in-degree = 0 但 out-degree > 0
Rejected: 收到 rejection 数 ≥ 2

4.2 Node Sizing

节点大小可以反映社会计量指标：

Mode	Size Rule	含义
Uniform (default)	所有节点相同大小 (r=20)	中性展示
By in-degree	r = 14 + in_degree × 4 (min: 14, max: 40)	越受欢迎越大
By betweenness	r = 14 + normalized_betweenness × 26	桥接角色越重要越大

DSL: config: sizing = in-degree 或在节点上 [size: large]

4.3 Node Coloring

Mode	Color Rule	含义
Default	All `#42A5F5` (blue)	中性
By group/category	按 group 属性着色	区分子组（班级、部门、性别等）
By role	Star=gold, Isolate=gray, Normal=blue	突出社会地位
By custom attribute	用户自定义	任意分类维度

Default color palette for groups (最多 8 组):

group1: #42A5F5 (blue)
group2: #66BB6A (green)
group3: #FFA726 (orange)
group4: #AB47BC (purple)
group5: #EF5350 (red)
group6: #26C6DA (cyan)
group7: #FFEE58 (yellow)
group8: #8D6E63 (brown)

4.4 Node Labels

Element	Position	Font	含义
Name/ID	Below node center, 4px gap	11px, `font-family: sans-serif`	Primary identifier
Role badge	Top-right corner	9px	Optional: ★ star, ● isolate
Details	Below name	9px, gray	Optional: age, title, etc.

5. Edge Types (Connection Lines)

5.1 Relationship Direction

Type	Line Style	DSL Syntax	SVG	含义
One-way choice	Arrow →	`A -> B`	`<line>` + `marker-end="url(#arrow)"`	A 选择了 B
Mutual choice	Double arrow ↔	`A <-> B`	`<line>` + both markers	相互选择
Undirected	Plain line —	`A -- B`	`<line>` without markers	已知关系，方向未知

5.2 Relationship Valence (正/负)

Type	Line Style	DSL Syntax	SVG	含义
Positive/attraction	Solid line	`->` / `<->` / `--`	`<line>` solid, color: `#388E3C` (green)	选择/喜欢/信任
Negative/rejection	Dashed red line	`-x>` / `<x->` / `-x-`	`<line>` dashed, color: `#D32F2F` (red)	拒绝/冲突/回避
Neutral/indifferent	Dotted gray line	`-.>` / `<.->` / `-.-`	`<line>` dotted, color: `#9E9E9E` (gray)	中性/无明确态度

5.3 Edge Weight (Relationship Strength)

Weight	Line Width	DSL Syntax	含义
Weak (1)	1px	`A -> B [weight: 1]`	弱连接
Normal (2, default)	2px	`A -> B`	一般连接
Strong (3)	3.5px	`A -> B [weight: 3]` 或 `A ==> B`	强连接
Very strong (4+)	5px	`A -> B [weight: 4]` 或 `A ===> B`	非常强连接

5.4 Edge Labels

A -> B [label: "best friend"]
C -x> D [label: "bullying"]
E <-> F [label: "study partners"]

5.5 Combined DSL Examples

# One-way positive choice
alice -> bob

# Mutual strong positive
alice <==> carol

# One-way rejection
dave -x> eve

# Mutual neutral
frank <.-> grace

# Weighted with label
alice -> bob [weight: 3, label: "trusted advisor"]

6. Structural Patterns (Auto-Detected)

Schematex 应自动检测并可选标注以下经典社会计量结构：

6.1 Individual-Level Patterns

Pattern	Detection Rule	Visual Annotation
Star	in-degree ≥ mean + 1.5σ	Gold fill / ★ badge
Isolate	in-degree = 0 AND out-degree = 0	Dashed border, gray fill
Neglectee	in-degree = 0, out-degree > 0	Dashed border, blue fill
Rejected	rejection count ≥ 2	Red dashed border

6.2 Pair-Level Patterns

Pattern	Detection Rule	Visual Annotation
Mutual pair	A→B AND B→A	Thicker bidirectional line
Asymmetric pair	A→B but NOT B→A	Standard arrow

6.3 Group-Level Patterns

Pattern	Detection Rule	Visual Annotation
Clique	Subgroup where all members mutually choose each other (≥3 members)	Shaded convex hull background
Chain	A→B→C→... (unidirectional sequence, no mutual)	Sequential arrow path highlighted
Bridge	Node connecting two otherwise separate clusters	Diamond shape overlay or highlight ring

DSL 控制: config: highlight = stars, isolates, cliques (默认: stars, isolates)

7. Layout Rules

7.1 Layout Algorithm Options

Sociogram 支持多种布局，不同场景适用性不同：

Layout	算法	适用场景	复杂度
Force-directed (default)	Fruchterman-Reingold / spring model	通用群体网络，自动聚类	O(n² × iterations)
Circular	均匀排列在圆周上	小组（≤15人），强调谁连接了谁	O(n)
Concentric	按 in-degree 分层圆环	强调核心-边缘结构	O(n log n)
Group-based	按 group 属性分区	跨组关系可视化	O(n) + force within group

7.2 Force-Directed Layout (Default)

Fruchterman-Reingold 算法实现：

初始化：节点随机放置在画布内
循环 max_iterations 次：
  对每对节点计算 repulsive force (f_rep = k²/d)
  对每条边计算 attractive force (f_att = d²/k)
  更新节点位置（clamp to canvas bounds）
  逐步降低 temperature（模拟退火）

Parameter	Default Value	含义
k (optimal distance)	`sqrt(canvas_area / node_count)`	节点间理想距离
max_iterations	300	收敛步数
initial_temperature	canvas_width / 10	初始位移上限
cooling_rate	0.95	每步温度衰减
min_distance	60px	节点最小间距（硬约束）

7.3 Circular Layout

角度间隔 = 2π / node_count
第 i 个节点位置：
  x = center_x + radius × cos(i × 角度间隔 - π/2)
  y = center_y + radius × sin(i × 角度间隔 - π/2)

Parameter	Default Value	含义
Radius	max(120, node_count × 20)	圆的半径
Start angle	-π/2 (12 o'clock)	第一个节点的起始位置

排序优化： 按 group 属性聚集相邻位置，减少跨组连线交叉。

7.4 Concentric Layout

按社会地位分层：

Ring 0 (center):  Stars (in-degree 最高)
Ring 1:           Above-average in-degree
Ring 2:           Average in-degree
Ring 3 (outer):   Below-average + isolates

Parameter	Default Value
Ring 0 radius	0px (单个 star 放中心) 或 40px (多个)
Ring gap	80px
Outer ring radius	ring_count × 80px

7.5 Spacing & Canvas Rules

Parameter	Default	含义
Node radius	20px (uniform)	默认节点大小
Min node-to-node gap	60px	避免重叠
Edge-to-node gap	2px	线不穿入节点
Canvas padding	50px	边缘留白
Label gap below node	4px	标签与节点间距
Arrow marker size	8px	箭头大小

7.6 Responsive Sizing

Group Size	Recommended Layout	Canvas Size
≤ 8	Circular	400 × 400
9-20	Force-directed 或 Circular	600 × 600
21-40	Force-directed	800 × 800
41+	Force-directed + group clustering	1000 × 1000+

8. DSL Grammar (Sociogram)

document        = header config* group_def* node_def* edge_def*
header          = "sociogram" quoted_string? NEWLINE

config          = "config:" config_key "=" config_value NEWLINE
config_key      = "layout" | "sizing" | "highlight" | "coloring"
config_value    = /[a-zA-Z0-9_, -]+/

group_def       = "group" ID properties? NEWLINE
                  INDENT node_ref+ DEDENT

node_def        = ID properties? NEWLINE
properties      = "[" property ("," property)* "]"
property        = "label:" quoted_string
               | "group:" ID
               | "size:" SIZE
               | "role:" ROLE
               | kv_prop

SIZE            = "small" | "medium" | "large"
ROLE            = "star" | "isolate" | "bridge"

edge_def        = ID edge_op ID edge_props? NEWLINE
edge_op         = "->" | "<->" | "--"          (* positive *)
               | "-x>" | "<x->" | "-x-"       (* negative/rejection *)
               | "-.>" | "<.->" | "-.-"        (* neutral *)
               | "==>" | "<==>" | "==="        (* strong positive *)
               | "===>" | "<===>"              (* very strong positive *)
edge_props      = "[" edge_prop ("," edge_prop)* "]"
edge_prop       = "label:" quoted_string
               | "weight:" NUMBER

ID              = /[a-zA-Z][a-zA-Z0-9_-]*/
quoted_string   = '"' /[^"]*/ '"'
NUMBER          = /[0-9]+/
kv_prop         = IDENTIFIER ":" VALUE

9. Test Cases

Case 1: Basic Classroom Sociogram (Directed Choices)

sociogram "Mrs. Chen's 4th Grade Class"
  alice [label: "Alice"]
  bob [label: "Bob"]
  carol [label: "Carol"]
  dave [label: "Dave"]
  eve [label: "Eve"]
  frank [label: "Frank"]
  alice -> bob
  alice -> carol
  bob -> alice
  bob -> dave
  carol -> alice
  carol -> eve
  dave -> bob
  dave -> frank
  eve -> carol
  eve -> alice
  frank -> dave

验证：alice 是 star（in-degree 3），frank 是 neglectee（in-degree 1, 仅被 dave 选）。alice ↔ bob 和 alice ↔ carol 是 mutual pairs。

Case 2: With Groups and Rejection (Bullying Analysis)

sociogram "Playground Dynamics"
  config: layout = force-directed
  config: highlight = stars, isolates, cliques
  config: coloring = group

  group boys [label: "Boys", color: "#42A5F5"]
    tom
    jack
    mike
    leo

  group girls [label: "Girls", color: "#EF5350"]
    anna
    beth
    chloe
    diana

  tom <-> jack
  tom -> mike
  jack -> leo
  mike -x> leo [label: "conflict"]
  anna <-> beth
  anna <-> chloe
  beth <-> chloe
  anna -> diana
  diana -.- tom
  leo -.- anna

验证：anna-beth-chloe 形成 clique（三人互选）。leo 接近 isolate（仅 jack 单向选择）。mike → leo 是 rejection（红色虚线）。diana 和 tom 之间是 neutral。

Case 3: Organizational Influence Map

sociogram "Engineering Team Informal Influence"
  config: layout = concentric
  config: sizing = in-degree

  ceo [label: "CEO", group: leadership]
  vp [label: "VP Eng", group: leadership]
  lead1 [label: "Tech Lead A", group: team-a]
  lead2 [label: "Tech Lead B", group: team-b]
  dev1 [label: "Senior Dev", group: team-a]
  dev2 [label: "Dev", group: team-a]
  dev3 [label: "Dev", group: team-b]
  dev4 [label: "Junior Dev", group: team-b]
  ops [label: "DevOps", group: infra]

  dev1 -> lead1
  dev2 -> lead1
  dev2 -> dev1
  dev3 -> lead2
  dev4 -> dev3
  lead1 -> vp
  lead2 -> vp
  vp -> ceo
  dev1 -> ops [label: "deployment help"]
  dev3 -> ops [label: "infra questions"]
  lead1 <-> lead2 [label: "weekly sync"]
  dev4 -> dev1 [label: "mentorship"]

验证：concentric 布局中 lead1 和 vp 应在内圈（高 in-degree），dev4 在外圈。ops 是 bridge（连接 team-a 和 team-b）。

sociogram "Group Therapy Session 5 - Trust Network"
  config: layout = circular

  therapist [label: "Dr. Park", role: star]
  james [label: "James"]
  maria [label: "Maria"]
  lee [label: "Lee"]
  sarah [label: "Sarah"]
  tom [label: "Tom"]
  nina [label: "Nina"]

  james -> therapist
  james <-> maria [weight: 3, label: "strong bond"]
  james -> lee
  maria -> therapist
  maria -> sarah
  lee -> therapist
  lee -.- nina
  sarah <-> nina
  sarah -> therapist
  tom -> therapist
  nina -> maria

验证：circular 布局，therapist 是 star。james ↔ maria 是 strong mutual pair（粗线）。tom 接近 isolate（只连接了 therapist）。lee 和 nina 之间是 neutral。

Case 5: Criminal Network Analysis

sociogram "Operation Sunset - Communication Network"
  config: layout = force-directed
  config: sizing = betweenness

  boss [label: "Subject Alpha"]
  lt1 [label: "Lieutenant 1"]
  lt2 [label: "Lieutenant 2"]
  courier1 [label: "Courier A"]
  courier2 [label: "Courier B"]
  contact1 [label: "External Contact 1"]
  contact2 [label: "External Contact 2"]
  associate1 [label: "Associate"]
  associate2 [label: "Associate"]

  boss <-> lt1 [weight: 4]
  boss <-> lt2 [weight: 4]
  lt1 -> courier1
  lt1 -> courier2
  lt2 -> associate1
  lt2 -> associate2
  courier1 -> contact1 [label: "supplier"]
  courier2 -> contact2 [label: "distributor"]
  lt1 <-> lt2 [weight: 2]
  associate1 -.- courier1

验证：boss 和 lt1 的 betweenness 最高（节点最大）。courier1 是 bridge（连接 lt1 和 contact1）。层级结构应在 force-directed 中自然呈现。

Case 6: Large Group Stress Test (30 nodes)

sociogram "Conference Networking"
  config: layout = force-directed

  p1 [label: "Person 1", group: a]
  p2 [label: "Person 2", group: a]
  p3 [label: "Person 3", group: a]
  p4 [label: "Person 4", group: a]
  p5 [label: "Person 5", group: a]
  p6 [label: "Person 6", group: b]
  p7 [label: "Person 7", group: b]
  p8 [label: "Person 8", group: b]
  p9 [label: "Person 9", group: b]
  p10 [label: "Person 10", group: b]
  p11 [label: "Person 11", group: c]
  p12 [label: "Person 12", group: c]
  p13 [label: "Person 13", group: c]
  p14 [label: "Person 14", group: c]
  p15 [label: "Person 15", group: c]
  p16 [label: "Person 16", group: d]
  p17 [label: "Person 17", group: d]
  p18 [label: "Person 18", group: d]
  p19 [label: "Person 19", group: d]
  p20 [label: "Person 20", group: d]
  p21 [label: "Person 21"]
  p22 [label: "Person 22"]
  p23 [label: "Person 23"]
  p24 [label: "Person 24"]
  p25 [label: "Person 25"]
  p26 [label: "Person 26"]
  p27 [label: "Person 27"]
  p28 [label: "Person 28"]
  p29 [label: "Person 29"]
  p30 [label: "Person 30"]
  p1 <-> p2
  p1 <-> p3
  p2 <-> p4
  p3 <-> p5
  p4 <-> p5
  p6 <-> p7
  p6 <-> p8
  p7 <-> p9
  p8 <-> p10
  p11 <-> p12
  p11 <-> p13
  p12 <-> p14
  p13 <-> p15
  p16 <-> p17
  p16 <-> p18
  p17 <-> p19
  p18 <-> p20
  p1 -> p6 [label: "cross-group"]
  p6 -> p11 [label: "cross-group"]
  p11 -> p16 [label: "cross-group"]
  p21 -> p1
  p22 -> p6
  p23 -> p11
  p24 -> p16
  p25 -- p26
  p27 -- p28
  p29 -- p30

验证：30 节点 → 自动 800×800 canvas。4 个 group 应通过 force-directed 自然聚类。p1、p6、p11、p16 是 cross-group bridges。p25-p30 是独立 pairs。

10. SVG Implementation Details

10.1 Arrow Markers

<defs>
  <!-- Positive arrow (dark gray) -->
  <marker id="sociogram-arrow" viewBox="0 0 10 10" refX="9" refY="5"
          markerWidth="8" markerHeight="8" orient="auto">
    <path d="M 0 0 L 10 5 L 0 10 z" fill="#333"/>
  </marker>
  <!-- Rejection arrow (red) -->
  <marker id="sociogram-arrow-reject" viewBox="0 0 10 10" refX="9" refY="5"
          markerWidth="8" markerHeight="8" orient="auto">
    <path d="M 0 0 L 10 5 L 0 10 z" fill="#D32F2F"/>
  </marker>
  <!-- Neutral arrow (gray) -->
  <marker id="sociogram-arrow-neutral" viewBox="0 0 10 10" refX="9" refY="5"
          markerWidth="8" markerHeight="8" orient="auto">
    <path d="M 0 0 L 10 5 L 0 10 z" fill="#9E9E9E"/>
  </marker>
</defs>

10.2 Edge Rendering

Edge-to-edge calculation (同 ecomap)：

线从节点边缘到节点边缘，不是中心到中心
计算方式：(center_A, center_B) 连线上，减去各自 radius + marker size

Bidirectional edges：

Mutual choice (<->)：两端都有 marker，用单条线
避免重叠：如果 A→B 和 B→A 都是单向但不是 mutual，画两条略微弯曲的线（offset ±3px）

Self-referential edges：

不支持（sociogram 不需要自指关系）

10.3 Clique Highlighting

当 config: highlight = cliques 时：

检测所有 cliques（完全子图，≥3 nodes）
对每个 clique，计算 convex hull
渲染半透明背景 <polygon> + 圆角处理

<polygon points="..." fill="#42A5F5" fill-opacity="0.08"
         stroke="#42A5F5" stroke-opacity="0.2" stroke-width="1"
         class="schematex-sociogram-clique"/>

10.4 CSS Classes

.schematex-sociogram-node { }
.schematex-sociogram-node-star { }
.schematex-sociogram-node-isolate { }
.schematex-sociogram-edge { }
.schematex-sociogram-edge-positive { }
.schematex-sociogram-edge-negative { }
.schematex-sociogram-edge-neutral { }
.schematex-sociogram-label { }
.schematex-sociogram-clique { }
.schematex-sociogram-group-label { }

Priority	Feature	Complexity	复用
P0 (Phase 3)	Circular layout + directed edges + 3 valence types	Medium	Arrow markers 复用 ecomap
P0	Node auto-detection (star/isolate)	Low	纯数据计算
P1	Force-directed layout (Fruchterman-Reingold)	High	新算法，但公式明确
P1	Group coloring + group-based node clustering	Medium	Color palette 复用 ecomap
P1	Edge weight → line thickness	Low
P2	Concentric layout	Medium	基于 radial 改造
P2	Clique detection + convex hull highlighting	High	图论算法
P2	Node sizing by metric (in-degree/betweenness)	Medium
P3	Edge labels	Low	复用 ecomap
P3	Social Atom variant (egocentric view)	Low	复用 ecomap radial
P3	Bridge detection	Medium	Betweenness centrality

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