Visualizing Delegation Hierarchies

Effective visualization of delegation hierarchies needs to communicate multiple dimensions simultaneously: structure (who delegates to whom), risk (which components are dangerous), permissions (what access each component has), and depth (how deep the delegation chains go). No single visualization approach excels at all of these.

The Visualization Challenge

A delegation risk diagram must convey:

Dimension	What It Means	Visual Challenge
Hierarchy	Parent-child delegation relationships	Standard tree problem
Risk level	Expected harm from each component	Needs color, size, or annotation
Permissions	Read/write/execute/network access	Multiple boolean attributes
Variable depth	Some chains are deep, others shallow	Asymmetric layouts
Cross-connections	Coordination between branches	Edges that break tree structure
Scale	Real systems have dozens to hundreds of nodes	Cognitive load management

Key Interactive Examples

Before diving into details, explore these representative examples:

Type	Best Example	What It Shows
Tree Diagrams	D3 Collapsible Tree	Click to expand/collapse
Treemaps	FinViz Stock Map	Size = value, color = change
Circle Packing	D3 Zoomable Circle Packing	Nested containment
Icicle Plots	D3 Zoomable Icicle	Width = size, depth = level
Risk-Specific	MITRE ATT&CK Navigator	Attack technique heatmap

For a comprehensive comparison: Hierarchy Visualization Comparison Tool

Classic Tree Diagrams (Node-Link)

The traditional approach: nodes connected by edges showing parent-child relationships.

Classic organizational hierarchy - the visual metaphor most people recognize

Basic Example

flowchart TD
    H[Human Principal] --> O[Orchestrator]
    O --> A[Agent A]
    O --> B[Agent B]
    O --> C[Agent C]
    A --> A1[Worker 1]
    A --> A2[Worker 2]
    B --> B1[Worker 3]
    C --> C1[Worker 4]
    C --> C2[Worker 5]
    C --> C3[Worker 6]

With Risk Encoding (Color + Annotations)

flowchart TD
    H[🏛️ Human Principal]
    H --> O[⚠️ Orchestrator]
    O --> A[Agent A]
    O --> B[Agent B]
    O --> C[⚠️ Agent C]
    A --> A1[Worker 1]
    A --> A2[Worker 2]
    B --> B1[Worker 3]
    C --> C1[Worker 4]
    C --> C2[⚠️ Worker 5]
    C --> C3[Worker 6]

    style H fill:#e3f2fd
    style O fill:#fff3e0
    style C fill:#fff3e0
    style C2 fill:#ffebee
    style A fill:#e8f5e9
    style B fill:#e8f5e9
    style A1 fill:#e8f5e9
    style A2 fill:#e8f5e9
    style B1 fill:#e8f5e9
    style C1 fill:#e8f5e9
    style C3 fill:#e8f5e9

Legend: Blue = oversight, Green = low risk, Orange = elevated risk, Red = high risk

Variable Depth Example

Real delegation trees are asymmetric—some branches go deep, others are shallow:

flowchart TD
    H[Human] --> C1[Coordinator]
    H --> C2[Coordinator]

    C1 --> D1[Deep Branch]
    D1 --> D2[Level 3]
    D2 --> D3[Level 4]
    D3 --> D4[Level 5]
    D4 --> D5[Level 6]

    C2 --> S1[Shallow Task]
    C2 --> S2[Shallow Task]

    C1 --> M1[Medium Branch]
    M1 --> M2[Level 3]
    M2 --> M3[Level 4]

Strengths:

Intuitive—most people can read tree diagrams immediately
Clear path tracing from root to any leaf
Easy to add annotations (colors, sizes, labels)
Works well for small-to-medium hierarchies (up to ~50 nodes)

Weaknesses:

Space-inefficient (lots of whitespace)
Deep trees become very tall or very wide
Cross-connections create visual clutter

Best for: Communicating structure to general audiences, interactive diagrams where users can expand/collapse

Research note: Nielsen Norman Group confirms node-link diagrams remain the most intuitive for tracing hierarchical paths.

Interactive Examples

D3 Collapsible Tree — Click to expand/collapse branches
D3 Tidy Tree — Clean algorithmic layout

Space-Filling Approaches

These techniques use all available space, encoding hierarchy through nesting rather than edges.

US exports by category (2017) - size shows export value, color shows category

Treemaps

Invented by Ben Shneiderman in 1990, treemaps represent hierarchy as nested rectangles. Rectangle size encodes a quantitative value (e.g., risk budget, compute allocation).

Conceptual Layout:

┌─────────────────────────────────────────────────┐
│                   Root System                    │
├─────────────────────┬───────────────────────────┤
│                     │                           │
│    Agent A (40%)    │      Agent B (35%)        │
│  ┌───────┬───────┐  │  ┌─────────────────────┐  │
│  │ W1    │ W2    │  │  │                     │  │
│  │ (25%) │ (15%) │  │  │     W3 (35%)        │  │
│  └───────┴───────┘  │  │                     │  │
│                     │  └─────────────────────┘  │
├─────────────────────┴───────────────────────────┤
│              Agent C (25%)                       │
│  ┌─────────┬─────────┬─────────┐                │
│  │ W4 (8%) │ W5 (10%)│ W6 (7%) │                │
│  └─────────┴─────────┴─────────┘                │
└─────────────────────────────────────────────────┘

Real-world example: FinViz Stock Market Treemap — Shows market sectors and stock performance using size and color.

For delegation risk: Rectangle size = risk budget allocation, color = risk type or status.

Interactive Examples:

D3 Zoomable Treemap — Click to zoom into sections
Treemap of Flare Classes — Software package hierarchy

Icicle Plots

Horizontal rectangles cascading downward (or sideways). Width encodes size, vertical position encodes depth.

Conceptual Layout:

┌─────────────────────────────────────────────────────┐
│                    Root (100%)                       │
├──────────────────────┬──────────────────┬───────────┤
│    Agent A (40%)     │  Agent B (35%)   │ C (25%)   │
├───────────┬──────────┼──────────────────┼─────┬─────┤
│ W1 (25%)  │ W2 (15%) │    W3 (35%)      │W4   │W5   │
├───────────┴──────────┴──────────────────┴─────┴─────┤
│                    (leaf level)                      │
└─────────────────────────────────────────────────────┘

Key advantage: Research found icicle plots outperformed treemaps and sunbursts for hierarchy understanding tasks.

For delegation risk: Width = risk budget or capability scope, color = risk level, depth = delegation chain length.

Interactive Examples:

D3 Zoomable Icicle — Click to zoom, shows 3 levels at a time
Icicle Chart Component — Standalone web component

Circle Packing

Nested circles where children are packed inside their parent circle.

Conceptual Layout:

        ╭───────────────────────────────────╮
       ╱                                     ╲
      │    ╭─────────╮    ╭───────────────╮   │
      │   ╱           ╲  ╱                 ╲  │
      │  │  ╭───╮╭───╮│ │ ╭─────╮╭──────╮ │  │
      │  │  │ W1││ W2││ │ │ W3  ││  W4  │ │  │
      │  │  ╰───╯╰───╯│ │ ╰─────╯╰──────╯ │  │
      │   ╲  Agent A ╱   ╲    Agent B    ╱   │
      │    ╰─────────╯    ╰──────────────╯   │
       ╲              Root                  ╱
        ╰───────────────────────────────────╯

The “wasted” space actually helps reveal hierarchy better than treemaps—containment is visually obvious.

For delegation risk: The visual metaphor of “containing risk within boundaries” aligns naturally with framework concepts.

Interactive Examples:

D3 Zoomable Circle Packing — Click to zoom in/out
D3 Circle Packing — Static version
Circle Packing Gallery — Multiple examples with code

Radial Approaches

Sunburst Charts

Concentric rings divided into segments, like a multi-layer pie chart.

pie title Risk Budget Allocation (Sunburst would show nested rings)
    "Agent A" : 40
    "Agent B" : 35
    "Agent C" : 25

(Mermaid doesn’t support true sunbursts—see interactive examples below)

Interactive Examples:

D3 Zoomable Sunburst — Click segments to zoom
D3 Sunburst — Static version

For delegation risk: Less recommended. Arc lengths are harder to compare than rectangles, and research indicates rectangular layouts are often clearer.

Chord Diagrams / Circos Plots

Nodes arranged on a circle, with arcs (chords) connecting related nodes. Excellent for showing cross-connections.

Interactive Examples:

D3 Chord Diagram — Shows flows between groups
Circos — The original genomics visualization tool

For delegation risk: Good for showing cross-branch coordination paths that break the tree structure.

Risk-Specific Visualizations

Beyond general hierarchy techniques, some visualizations are designed specifically for risk:

Fault Trees

Standard in nuclear and aerospace safety. AND/OR gates show how component failures combine:

flowchart TD
    TOP[🎯 System Failure]
    TOP --- OR1[OR Gate]

    OR1 --- PATH1[Path 1: All checks fail]
    OR1 --- PATH2[Path 2: Coordinator compromised]

    PATH1 --- AND1[AND Gate]
    AND1 --- A1[Review fails]
    AND1 --- A2[Tests fail]
    AND1 --- A3[Human approves]

    PATH2 --- AND2[AND Gate]
    AND2 --- B1[Coordinator schemes]
    AND2 --- B2[Evades monitoring]

For delegation risk: Directly applicable. See Nuclear Safety PRA for examples.

Bow-Tie Diagrams

Shows causes on the left, the risk event in the center, and consequences on the right:

Bow-tie diagram showing threats, barriers, event, and consequences (Wikimedia Commons)

flowchart LR
    subgraph Causes
        C1[Capability too high]
        C2[Permissions too broad]
        C3[Monitoring gaps]
    end

    subgraph Controls["Preventive Controls"]
        P1[Capability limits]
        P2[Permission boundaries]
    end

    C1 --> P1
    C2 --> P2
    C3 --> P2

    P1 --> EVENT[⚠️ Harmful Action]
    P2 --> EVENT

    EVENT --> M1[Detection]
    EVENT --> M2[Containment]

    subgraph Mitigations["Mitigating Controls"]
        M1
        M2
    end

    M1 --> CONS1[Limited damage]
    M2 --> CONS2[Stopped spread]

    subgraph Consequences
        CONS1
        CONS2
    end

For delegation risk: Shows the full picture—what leads to harm, what prevents it, what limits damage.

Risk Heat Maps / Matrices

The classic likelihood × impact matrix:

Simple risk matrix - likelihood vs. impact with color-coded severity (Wikimedia Commons)

quadrantChart
    title Risk Assessment Matrix
    x-axis Low Impact --> High Impact
    y-axis Low Likelihood --> High Likelihood
    quadrant-1 High Risk - Act Now
    quadrant-2 Medium Risk - Plan
    quadrant-3 Low Risk - Accept
    quadrant-4 Medium Risk - Monitor
    Agent A: [0.3, 0.2]
    Agent B: [0.6, 0.4]
    Agent C: [0.8, 0.7]
    Coordinator: [0.5, 0.8]

For delegation risk: Useful for comparing components, less useful for showing hierarchy.

Security Industry Visualization Approaches

The IT security industry has developed sophisticated visualization techniques for showing risk, attack paths, and system relationships. Many of these directly apply to delegation risk.

Attack Path Graphs

Security tools visualize how attackers can traverse systems to reach high-value targets. This maps directly to delegation chains.

Attack tree showing paths to system compromise (Wikimedia Commons)

flowchart LR
    subgraph "Attack Path View"
        Entry[🌐 Internet-Exposed<br/>Service] --> Vuln1[Vulnerable<br/>Container]
        Vuln1 --> Priv[Privilege<br/>Escalation]
        Priv --> Lateral[Lateral<br/>Movement]
        Lateral --> Crown[👑 Crown Jewels<br/>Database]
    end

    style Entry fill:#ffebee
    style Vuln1 fill:#fff3e0
    style Priv fill:#fff3e0
    style Lateral fill:#fff3e0
    style Crown fill:#ffcdd2,stroke:#c62828,stroke-width:3px

For delegation risk: Model delegation chains as attack paths. “Shortest path to catastrophic harm” = which component chain could cause maximum damage fastest?

Blast Radius Visualization

“Blast radius” shows the extent of damage if a component is compromised—what else is affected?

flowchart TD
    subgraph "Blast Radius from Compromised Coordinator"
        C[💥 Compromised<br/>Coordinator]
        C --> A1[Affected Agent 1]
        C --> A2[Affected Agent 2]
        C --> A3[Affected Agent 3]
        A1 --> W1[Worker 1]
        A1 --> W2[Worker 2]
        A2 --> W3[Worker 3]
        A3 --> W4[Worker 4]
        A3 --> W5[Worker 5]
    end

    style C fill:#d32f2f,color:#fff
    style A1 fill:#ff8a80
    style A2 fill:#ff8a80
    style A3 fill:#ff8a80
    style W1 fill:#ffcdd2
    style W2 fill:#ffcdd2
    style W3 fill:#ffcdd2
    style W4 fill:#ffcdd2
    style W5 fill:#ffcdd2

For delegation risk: “If this coordinator defects, what’s exposed?” Expand outward from any node to show everything in its delegation subtree.

MITRE ATT&CK Navigator (Coverage Heatmaps)

The MITRE ATT&CK Navigator is a matrix heatmap showing attack techniques vs. tactics, color-coded by coverage, frequency, or risk.

Example of a matrix heatmap - similar visual style to MITRE ATT&CK Navigator (Wikimedia Commons)

Initial Access	Execution	Persistence	Priv Esc	Defense Evasion	Lateral Movement
🟢 Low	🟡 Med	🟢 Low	🔴 High	🟡 Med	🔴 High
🟢 Low	🟢 Low	🟡 Med	🟡 Med	🔴 High	🟡 Med
🟡 Med	🔴 High	🟢 Low	🟢 Low	🟡 Med	🟢 Low

Each cell represents a technique; color indicates risk/coverage level

Features:

Overlay multiple “layers” (your coverage, adversary TTPs, gaps)
Color intensity shows severity or frequency
Interactive filtering and annotation

For delegation risk: Create a matrix of components vs. harm types. Color = risk level. Overlay accident risk and defection risk as separate layers.

Try it: MITRE ATT&CK Navigator

Cyber Kill Chain (Stage Diagrams)

Lockheed Martin’s Cyber Kill Chain shows attack progression as linear stages, with defenses mapped to each stage.

The Unified Kill Chain - an expanded model combining multiple frameworks (Wikimedia Commons)

flowchart LR
    subgraph "Cyber Kill Chain"
        R[1. Recon] --> W[2. Weaponize]
        W --> D[3. Deliver]
        D --> E[4. Exploit]
        E --> I[5. Install]
        I --> C[6. Command<br/>& Control]
        C --> A[7. Actions on<br/>Objectives]
    end

    subgraph "Defenses"
        R -.-> DR[Monitor exposure]
        D -.-> DD[Email filtering]
        E -.-> DE[Patch management]
        C -.-> DC[Network monitoring]
    end

For delegation risk: Map delegation stages (task receipt → decomposition → execution → aggregation → delivery) with controls at each stage.

Permission/Access Graphs

Security tools visualize who can access what, showing permission relationships as graphs.

flowchart TD
    subgraph "Permission Graph"
        U1[User A] -->|read| DB[(Database)]
        U1 -->|write| S1[Service 1]
        U2[User B] -->|admin| S1
        U2 -->|read| DB
        S1 -->|query| DB
        S2[Service 2] -->|read| DB
    end

    style DB fill:#e3f2fd
    style S1 fill:#fff3e0
    style S2 fill:#e8f5e9

For delegation risk: Show what each component can access. Edge labels = permission type. Identify over-privileged components.

Real-Time Network Topology

Common network topology patterns - security tools show these dynamically with risk overlays (Wikimedia Commons)

Tools like Riverside (open source) and Auvik show live network topology with traffic flow.

Key features:

Nodes appear/disappear as devices connect/disconnect
Edge thickness = traffic volume
Color = security status (normal/warning/alert)
Time-travel to replay historical states

For delegation risk: Show delegation graph evolving in real-time as tasks spawn subtasks. Replay to understand what happened during an incident.

Security Visualization Gallery

Visualization	Best For	Example Tool
Attack path graph	Showing routes to high-value targets	BloodHound
Blast radius	Impact analysis of compromised components	Wiz
Coverage heatmap	Gaps in defense coverage	MITRE Navigator
Kill chain stages	Linear progression with controls	Cyber Kill Chain
Permission graph	Access relationships	Varonis
Live topology	Real-time system state	Riverside
Risk matrix	Likelihood × Impact comparison	Miro templates

Adapting Security Visualizations for Delegation Risk

Security Concept	Delegation Risk Analog
Attack path to Domain Admin	Delegation chain to catastrophic harm
Blast radius of credential compromise	Impact zone if coordinator defects
MITRE technique coverage	Component coverage of harm modes
Kill chain stages	Task lifecycle stages
Permission graph	Component access rights
Choke points	High-leverage control points
Lateral movement	Cross-branch coordination

Encoding Risk and Permissions

Beyond structure, delegation diagrams need to encode risk levels and permissions:

Visual Variables for Risk

Variable	Example	Pros	Cons
Color hue	🔴 High → 🟡 Medium → 🟢 Low	Intuitive	Colorblind issues
Size	Larger = more risk	Very salient	Conflicts with hierarchy
Border thickness	Thicker = higher risk	Works with fill	Subtle
Warning badges	⚠️ on risky nodes	Clear meaning	Adds clutter

Visual Variables for Permissions

Variable	Example	Best For
Border style	Solid/dashed/dotted	Read/write/none
Fill pattern	Solid/outline/half	Access levels
Small icons	🔒 🔑 👁️	Semantic meaning

Combined Example

flowchart TD
    H["👤 Human<br/>Full Access"]
    H --> C["⚠️ Coordinator<br/>Read-All, Write-None"]
    C --> E1["Executor A<br/>Write: /src only"]
    C --> E2["Executor B<br/>Read-only"]
    C --> E3["⚠️ Executor C<br/>Network Access"]

    style H fill:#e3f2fd,stroke:#1565c0,stroke-width:3px
    style C fill:#fff3e0,stroke:#ef6c00,stroke-width:2px
    style E1 fill:#e8f5e9,stroke:#2e7d32,stroke-width:1px
    style E2 fill:#e8f5e9,stroke:#2e7d32,stroke-width:1px
    style E3 fill:#ffebee,stroke:#c62828,stroke-width:2px

Recommendations for Delegation Risk

Based on this survey:

For Documentation & Communication

Use: Node-link tree diagrams with:

Color gradient (warm = high risk, cool = low)
Warning badges on highest-risk nodes
Dotted lines for cross-branch coordination
Mermaid for simple diagrams, D3 for complex ones

For Dashboards & Monitoring

Consider: Icicle plots or treemaps with:

Width encoding risk budget
Color encoding status (green/yellow/red)
Interactive drill-down

For Interactive Exploration

Consider: D3 Zoomable Circle Packing or Collapsible Tree

Visualizing Delegation Hierarchies

Visualizing Delegation Hierarchies

The Visualization Challenge

Key Interactive Examples

Classic Tree Diagrams (Node-Link)

Basic Example

With Risk Encoding (Color + Annotations)

Variable Depth Example

Interactive Examples

Space-Filling Approaches

Treemaps

Icicle Plots

Circle Packing

Radial Approaches

Sunburst Charts

Chord Diagrams / Circos Plots

Risk-Specific Visualizations

Fault Trees

Bow-Tie Diagrams

Risk Heat Maps / Matrices

Security Industry Visualization Approaches

Attack Path Graphs

Blast Radius Visualization

MITRE ATT&CK Navigator (Coverage Heatmaps)

Cyber Kill Chain (Stage Diagrams)

Permission/Access Graphs

Real-Time Network Topology

Security Visualization Gallery

Adapting Security Visualizations for Delegation Risk

Encoding Risk and Permissions

Visual Variables for Risk

Visual Variables for Permissions

Combined Example

Recommendations for Delegation Risk

For Documentation & Communication

For Dashboards & Monitoring

For Interactive Exploration

Further Reading

Interactive Example Collections

Research Papers

Comparison Tools

Security Visualization Resources

See Also