# ADR-029: Graph Neural Network Integration for Claude-Flow V3

**Status:** Proposed
**Date:** 2026-01-16
**Author:** System Architecture Designer
**Version:** 1.0.0

## Context

Claude-Flow V3 processes complex, interconnected data structures that naturally form graphs:

1. **Codebase Dependency Graphs** - Files, modules, and packages with import/export relationships
2. **Agent Relationship Networks** - Agents with communication patterns, task delegation, and coordination
3. **Pattern Propagation** - How learned patterns spread through swarm topologies
4. **Impact Analysis** - Understanding ripple effects of code changes across the codebase

Current approaches using flat embeddings and HNSW indexing (ADR-017) excel at similarity search but fail to capture:

- **Structural relationships** between entities
- **Multi-hop dependencies** (A depends on B which depends on C)
- **Graph-level patterns** (subgraph isomorphism, community structures)
- **Edge semantics** (import vs. inheritance vs. composition)

The RuVector intelligence system already provides:
- AST analysis for individual files
- Complexity metrics
- MinCut/Louvain graph algorithms for code boundaries

However, these are hand-crafted algorithms that don't learn from data. GNN integration enables **learned graph representations** that improve with usage.

### Problem Statement

| Challenge | Current Limitation | GNN Solution |
|-----------|-------------------|--------------|
| Dependency tracking | Manual traversal, no learned patterns | GCN propagates dependency signals |
| Impact analysis | Static rules, misses indirect effects | Message passing captures multi-hop effects |
| Agent coordination | Fixed topologies | GAT learns optimal attention patterns |
| Pattern discovery | Per-file analysis only | Graph-level pooling finds structural patterns |

## Decision

Integrate Graph Neural Network layers from RuVector into Claude-Flow V3 for graph-aware processing. The integration follows the **optional dependency pattern** established in ADR-017.

### Design Principles

1. **Modular Architecture** - Each GNN layer type is independently usable
2. **Optional Integration** - Graceful fallback to non-GNN methods
3. **Memory-Efficient** - Sparse representations for large graphs
4. **Incremental Learning** - Online updates without full retraining
5. **Consistent API** - Matches existing RuVector interfaces

---

## GNN Layer Types

### 1. Graph Convolutional Networks (GCN)

**Purpose:** Propagate features through graph structure using spectral convolutions.

**Use Cases:**
- Codebase-wide feature propagation
- Transitive dependency resolution
- Global pattern aggregation

```typescript
// v3/@claude-flow/gnn/src/layers/gcn.ts

export interface GCNConfig {
  inputDim: number;
  hiddenDim: number;
  outputDim: number;
  numLayers: number;
  dropout?: number;
  activation?: 'relu' | 'leaky_relu' | 'gelu' | 'tanh';
  normalization?: 'symmetric' | 'left' | 'right';
  addSelfLoops?: boolean;
}

export interface GCNLayer {
  /**
   * Forward pass through GCN layer
   * @param nodeFeatures - Node feature matrix [N x inputDim]
   * @param adjacency - Sparse adjacency matrix [N x N]
   * @returns Updated node features [N x outputDim]
   */
  forward(
    nodeFeatures: Float32Array,
    adjacency: SparseMatrix
  ): Float32Array;

  /**
   * Backward pass for gradient computation
   */
  backward(
    gradOutput: Float32Array,
    nodeFeatures: Float32Array,
    adjacency: SparseMatrix
  ): GradientResult;

  /**
   * Get learnable parameters
   */
  parameters(): ParameterMap;
}

export class GraphConvolutionalNetwork implements GCNLayer {
  private weights: Float32Array[];
  private biases: Float32Array[];
  private config: GCNConfig;

  constructor(config: GCNConfig) {
    this.config = {
      dropout: 0.1,
      activation: 'relu',
      normalization: 'symmetric',
      addSelfLoops: true,
      ...config
    };
    this.initializeWeights();
  }

  forward(nodeFeatures: Float32Array, adjacency: SparseMatrix): Float32Array {
    let h = nodeFeatures;

    // Normalize adjacency matrix
    const normAdj = this.normalizeAdjacency(adjacency);

    for (let l = 0; l < this.config.numLayers; l++) {
      // Message passing: H' = σ(D^(-1/2) A D^(-1/2) H W)
      h = this.sparseMatmul(normAdj, h);
      h = this.dense(h, this.weights[l], this.biases[l]);
      h = this.activate(h);

      if (this.config.dropout && l < this.config.numLayers - 1) {
        h = this.dropout(h, this.config.dropout);
      }
    }

    return h;
  }

  private normalizeAdjacency(adj: SparseMatrix): SparseMatrix {
    // Add self-loops
    if (this.config.addSelfLoops) {
      adj = addIdentity(adj);
    }

    // Compute degree matrix
    const degree = computeDegree(adj);

    // Symmetric normalization: D^(-1/2) A D^(-1/2)
    return symmetricNormalize(adj, degree);
  }
}
```

### 2. Graph Attention Networks (GAT)

**Purpose:** Learn attention weights between connected nodes for adaptive message passing.

**Use Cases:**
- Agent coordination optimization
- Priority-weighted dependency analysis
- Selective pattern propagation

```typescript
// v3/@claude-flow/gnn/src/layers/gat.ts

export interface GATConfig {
  inputDim: number;
  outputDim: number;
  numHeads: number;
  headDim?: number;
  dropout?: number;
  attentionDropout?: number;
  leakyReluSlope?: number;
  concat?: boolean;  // Concatenate heads or average
  residual?: boolean;
}

export interface AttentionWeights {
  nodeIdx: number;
  neighborIdx: number;
  weight: number;
  headIdx: number;
}

export interface GATOutput {
  nodeFeatures: Float32Array;
  attentionWeights: AttentionWeights[];
}

export class GraphAttentionNetwork {
  private config: GATConfig;
  private Wq: Float32Array[];  // Query projections per head
  private Wk: Float32Array[];  // Key projections per head
  private Wv: Float32Array[];  // Value projections per head
  private attentionVector: Float32Array[];

  constructor(config: GATConfig) {
    this.config = {
      headDim: Math.floor(config.outputDim / config.numHeads),
      dropout: 0.1,
      attentionDropout: 0.1,
      leakyReluSlope: 0.2,
      concat: true,
      residual: true,
      ...config
    };
    this.initializeParameters();
  }

  forward(
    nodeFeatures: Float32Array,
    adjacency: SparseMatrix,
    returnAttention?: boolean
  ): GATOutput {
    const numNodes = nodeFeatures.length / this.config.inputDim;
    const headOutputs: Float32Array[] = [];
    const allAttentionWeights: AttentionWeights[] = [];

    for (let h = 0; h < this.config.numHeads; h++) {
      // Linear transformation for this head
      const queries = this.project(nodeFeatures, this.Wq[h]);
      const keys = this.project(nodeFeatures, this.Wk[h]);
      const values = this.project(nodeFeatures, this.Wv[h]);

      // Compute attention scores for connected pairs
      const { output, attention } = this.attentionAggregation(
        queries, keys, values, adjacency, h
      );

      headOutputs.push(output);
      if (returnAttention) {
        allAttentionWeights.push(...attention);
      }
    }

    // Combine heads
    let finalOutput: Float32Array;
    if (this.config.concat) {
      finalOutput = this.concatenateHeads(headOutputs);
    } else {
      finalOutput = this.averageHeads(headOutputs);
    }

    // Residual connection
    if (this.config.residual &&
        this.config.inputDim === finalOutput.length / numNodes) {
      finalOutput = this.addResidual(finalOutput, nodeFeatures);
    }

    return {
      nodeFeatures: finalOutput,
      attentionWeights: allAttentionWeights
    };
  }

  private attentionAggregation(
    queries: Float32Array,
    keys: Float32Array,
    values: Float32Array,
    adjacency: SparseMatrix,
    headIdx: number
  ): { output: Float32Array; attention: AttentionWeights[] } {
    const attention: AttentionWeights[] = [];
    const output = new Float32Array(values.length);

    // Iterate over nodes
    for (const [i, neighbors] of adjacency.rowIterator()) {
      const qi = this.getNodeVector(queries, i, this.config.headDim!);
      let sumWeights = 0;
      const scores: { j: number; score: number }[] = [];

      // Compute attention scores for neighbors
      for (const j of neighbors) {
        const kj = this.getNodeVector(keys, j, this.config.headDim!);
        const score = this.leakyRelu(
          this.dot(qi, kj) + this.dot(this.attentionVector[headIdx],
            this.concat(qi, kj))
        );
        scores.push({ j, score });
      }

      // Softmax over neighbors
      const maxScore = Math.max(...scores.map(s => s.score));
      const expScores = scores.map(s => ({
        j: s.j,
        exp: Math.exp(s.score - maxScore)
      }));
      const sumExp = expScores.reduce((sum, s) => sum + s.exp, 0);

      // Aggregate neighbor values
      for (const { j, exp } of expScores) {
        const weight = exp / sumExp;
        const vj = this.getNodeVector(values, j, this.config.headDim!);

        for (let d = 0; d < this.config.headDim!; d++) {
          output[i * this.config.headDim! + d] += weight * vj[d];
        }

        attention.push({ nodeIdx: i, neighborIdx: j, weight, headIdx });
      }
    }

    return { output, attention };
  }

  /**
   * Get interpretable attention patterns for analysis
   */
  getAttentionPatterns(
    adjacency: SparseMatrix,
    nodeLabels?: string[]
  ): AttentionPattern[] {
    // Returns top attention edges for visualization/debugging
  }
}
```

### 3. GraphSAGE (Sample and Aggregate)

**Purpose:** Inductive learning through neighborhood sampling - enables processing of unseen nodes.

**Use Cases:**
- New file/module analysis without full retraining
- Incremental codebase updates
- Scalable processing of large graphs

```typescript
// v3/@claude-flow/gnn/src/layers/graphsage.ts

export interface GraphSAGEConfig {
  inputDim: number;
  hiddenDim: number;
  outputDim: number;
  numLayers: number;
  sampleSizes: number[];  // Neighbors to sample at each layer
  aggregator: 'mean' | 'max' | 'lstm' | 'gcn';
  dropout?: number;
  normalize?: boolean;
}

export interface NeighborSampler {
  /**
   * Sample fixed number of neighbors for mini-batch training
   */
  sample(
    nodes: number[],
    adjacency: SparseMatrix,
    numSamples: number
  ): SampledSubgraph;
}

export interface SampledSubgraph {
  nodes: number[];
  edges: [number, number][];
  layerNodes: number[][];  // Nodes needed at each layer
}

export class GraphSAGE {
  private config: GraphSAGEConfig;
  private aggregators: Aggregator[];
  private sampler: NeighborSampler;

  constructor(config: GraphSAGEConfig) {
    this.config = {
      aggregator: 'mean',
      dropout: 0.1,
      normalize: true,
      ...config
    };

    if (config.sampleSizes.length !== config.numLayers) {
      throw new Error('sampleSizes length must match numLayers');
    }

    this.initializeAggregators();
    this.sampler = new UniformNeighborSampler();
  }

  /**
   * Full-batch forward pass (for small graphs)
   */
  forward(
    nodeFeatures: Float32Array,
    adjacency: SparseMatrix
  ): Float32Array {
    let h = nodeFeatures;

    for (let l = 0; l < this.config.numLayers; l++) {
      h = this.aggregateNeighbors(h, adjacency, l);
    }

    if (this.config.normalize) {
      h = this.l2Normalize(h);
    }

    return h;
  }

  /**
   * Mini-batch forward pass (for large graphs)
   */
  forwardMiniBatch(
    targetNodes: number[],
    nodeFeatures: Float32Array,
    adjacency: SparseMatrix
  ): Float32Array {
    // Sample computation graph
    const subgraph = this.sampleComputationGraph(targetNodes, adjacency);

    // Bottom-up aggregation
    let h = this.extractFeatures(nodeFeatures, subgraph.nodes);

    for (let l = this.config.numLayers - 1; l >= 0; l--) {
      const layerNodes = subgraph.layerNodes[l];
      h = this.aggregateNeighborsSampled(h, subgraph, l, layerNodes);
    }

    // Return only target node embeddings
    return this.extractTargetEmbeddings(h, targetNodes, subgraph);
  }

  private aggregateNeighbors(
    h: Float32Array,
    adjacency: SparseMatrix,
    layer: number
  ): Float32Array {
    const numNodes = h.length / this.currentDim(layer);
    const output = new Float32Array(numNodes * this.nextDim(layer));

    for (let i = 0; i < numNodes; i++) {
      const neighbors = adjacency.getRow(i);

      // Aggregate neighbor features
      const neighborFeatures = neighbors.map(j =>
        this.getNodeVector(h, j, this.currentDim(layer))
      );

      const aggregated = this.aggregators[layer].aggregate(neighborFeatures);

      // Combine with self features
      const selfFeatures = this.getNodeVector(h, i, this.currentDim(layer));
      const combined = this.combine(selfFeatures, aggregated, layer);

      this.setNodeVector(output, i, combined);
    }

    return output;
  }

  /**
   * Generate embeddings for new, unseen nodes
   */
  inductiveEmbed(
    newNodeFeatures: Float32Array,
    existingAdjacency: SparseMatrix,
    newEdges: [number, number][]
  ): Float32Array {
    // Extend adjacency with new nodes
    const extendedAdj = this.extendAdjacency(existingAdjacency, newEdges);

    // Forward pass only for new nodes
    const newNodeIds = this.getNewNodeIds(existingAdjacency, extendedAdj);
    return this.forwardMiniBatch(newNodeIds, newNodeFeatures, extendedAdj);
  }
}

/**
 * Aggregator implementations
 */
export class MeanAggregator implements Aggregator {
  aggregate(neighborFeatures: Float32Array[]): Float32Array {
    if (neighborFeatures.length === 0) {
      return new Float32Array(this.outputDim);
    }

    const result = new Float32Array(neighborFeatures[0].length);
    for (const features of neighborFeatures) {
      for (let i = 0; i < features.length; i++) {
        result[i] += features[i];
      }
    }

    for (let i = 0; i < result.length; i++) {
      result[i] /= neighborFeatures.length;
    }

    return result;
  }
}

export class MaxPoolAggregator implements Aggregator {
  private mlp: MLP;

  aggregate(neighborFeatures: Float32Array[]): Float32Array {
    // Transform then element-wise max
    const transformed = neighborFeatures.map(f => this.mlp.forward(f));
    return this.elementwiseMax(transformed);
  }
}

export class LSTMAggregator implements Aggregator {
  private lstm: LSTM;

  aggregate(neighborFeatures: Float32Array[]): Float32Array {
    // Order-invariant through random permutation during training
    const permuted = this.randomPermute(neighborFeatures);
    return this.lstm.forward(permuted);
  }
}
```

### 4. Message Passing Neural Networks (MPNN)

**Purpose:** General framework for learning on graphs with edge features.

**Use Cases:**
- Dependency type modeling (import, extends, implements)
- Agent communication patterns with message metadata
- Change impact with relationship strength

```typescript
// v3/@claude-flow/gnn/src/layers/mpnn.ts

export interface MPNNConfig {
  nodeDim: number;
  edgeDim: number;
  messageDim: number;
  hiddenDim: number;
  outputDim: number;
  numSteps: number;  // Message passing iterations
  messageFunction: 'mlp' | 'attention' | 'edge_network';
  updateFunction: 'gru' | 'lstm' | 'mlp';
  readoutFunction: 'sum' | 'mean' | 'max' | 'attention' | 'set2set';
}

export interface EdgeData {
  source: number;
  target: number;
  features: Float32Array;
}

export interface MessagePassingResult {
  nodeEmbeddings: Float32Array;
  graphEmbedding?: Float32Array;
  messageHistory?: MessageHistory[];
}

export class MessagePassingNetwork {
  private config: MPNNConfig;
  private messageNet: MessageNetwork;
  private updateNet: UpdateNetwork;
  private readoutNet: ReadoutNetwork;

  constructor(config: MPNNConfig) {
    this.config = config;
    this.initializeNetworks();
  }

  forward(
    nodeFeatures: Float32Array,
    edges: EdgeData[],
    computeGraphEmbedding?: boolean
  ): MessagePassingResult {
    let h = nodeFeatures;
    const history: MessageHistory[] = [];

    // Message passing iterations
    for (let t = 0; t < this.config.numSteps; t++) {
      const messages = this.computeMessages(h, edges);
      const aggregated = this.aggregateMessages(messages, h.length / this.config.nodeDim);
      h = this.updateNodes(h, aggregated);

      history.push({
        step: t,
        nodeStates: new Float32Array(h),
        messages: messages
      });
    }

    const result: MessagePassingResult = {
      nodeEmbeddings: h,
      messageHistory: history
    };

    if (computeGraphEmbedding) {
      result.graphEmbedding = this.readout(h);
    }

    return result;
  }

  private computeMessages(
    nodeStates: Float32Array,
    edges: EdgeData[]
  ): Message[] {
    const messages: Message[] = [];

    for (const edge of edges) {
      const sourceState = this.getNodeVector(nodeStates, edge.source);
      const targetState = this.getNodeVector(nodeStates, edge.target);

      // M_t(h_v, h_w, e_vw)
      const message = this.messageNet.compute(
        sourceState,
        targetState,
        edge.features
      );

      messages.push({
        source: edge.source,
        target: edge.target,
        content: message
      });
    }

    return messages;
  }

  private aggregateMessages(
    messages: Message[],
    numNodes: number
  ): Float32Array {
    const aggregated = new Float32Array(numNodes * this.config.messageDim);

    // Group messages by target
    const byTarget = new Map<number, Float32Array[]>();
    for (const msg of messages) {
      if (!byTarget.has(msg.target)) {
        byTarget.set(msg.target, []);
      }
      byTarget.get(msg.target)!.push(msg.content);
    }

    // Aggregate for each node
    for (const [target, nodeMessages] of byTarget) {
      const aggregatedMsg = this.sumMessages(nodeMessages);
      this.setNodeVector(aggregated, target, aggregatedMsg, this.config.messageDim);
    }

    return aggregated;
  }

  private updateNodes(
    currentStates: Float32Array,
    aggregatedMessages: Float32Array
  ): Float32Array {
    const numNodes = currentStates.length / this.config.nodeDim;
    const newStates = new Float32Array(numNodes * this.config.hiddenDim);

    for (let i = 0; i < numNodes; i++) {
      const h = this.getNodeVector(currentStates, i, this.config.nodeDim);
      const m = this.getNodeVector(aggregatedMessages, i, this.config.messageDim);

      // h_v^(t+1) = U_t(h_v^t, m_v^(t+1))
      const updated = this.updateNet.update(h, m);
      this.setNodeVector(newStates, i, updated, this.config.hiddenDim);
    }

    return newStates;
  }

  private readout(finalStates: Float32Array): Float32Array {
    // R = Σ_v r(h_v^T)
    return this.readoutNet.aggregate(finalStates);
  }
}

/**
 * Edge Network for computing messages based on edge features
 */
export class EdgeNetwork implements MessageNetwork {
  private edgeMLP: MLP;

  compute(
    sourceState: Float32Array,
    targetState: Float32Array,
    edgeFeatures: Float32Array
  ): Float32Array {
    // A(e_vw) transforms edge features into a matrix
    const edgeMatrix = this.edgeMLP.forward(edgeFeatures);

    // Message = A(e_vw) * h_v
    return this.matmul(edgeMatrix, sourceState);
  }
}
```

### 5. Edge Convolution (EdgeConv)

**Purpose:** Dynamic graph convolution that learns edge features from node pairs.

**Use Cases:**
- Discovering implicit relationships
- Learning dependency strength
- Dynamic topology adaptation

```typescript
// v3/@claude-flow/gnn/src/layers/edge-conv.ts

export interface EdgeConvConfig {
  inputDim: number;
  outputDim: number;
  hiddenDims: number[];
  k?: number;  // k-nearest neighbors (for dynamic graph)
  aggregation: 'max' | 'mean' | 'sum';
  dynamicGraph?: boolean;
}

export class EdgeConvolution {
  private config: EdgeConvConfig;
  private edgeMLP: MLP;

  constructor(config: EdgeConvConfig) {
    this.config = {
      k: 20,
      aggregation: 'max',
      dynamicGraph: false,
      ...config
    };
    this.initializeMLP();
  }

  forward(
    nodeFeatures: Float32Array,
    adjacency?: SparseMatrix
  ): Float32Array {
    const numNodes = nodeFeatures.length / this.config.inputDim;

    // Build dynamic graph if needed
    let adj = adjacency;
    if (this.config.dynamicGraph || !adjacency) {
      adj = this.buildKNNGraph(nodeFeatures);
    }

    const output = new Float32Array(numNodes * this.config.outputDim);

    for (let i = 0; i < numNodes; i++) {
      const xi = this.getNodeVector(nodeFeatures, i);
      const neighbors = adj!.getRow(i);

      const edgeFeatures: Float32Array[] = [];

      for (const j of neighbors) {
        const xj = this.getNodeVector(nodeFeatures, j);

        // Edge feature: [xj - xi, xi] (relative + absolute)
        const diff = this.subtract(xj, xi);
        const edgeInput = this.concat(diff, xi);

        // Transform through MLP
        const transformed = this.edgeMLP.forward(edgeInput);
        edgeFeatures.push(transformed);
      }

      // Aggregate edge features
      const aggregated = this.aggregate(edgeFeatures);
      this.setNodeVector(output, i, aggregated);
    }

    return output;
  }

  private buildKNNGraph(nodeFeatures: Float32Array): SparseMatrix {
    const numNodes = nodeFeatures.length / this.config.inputDim;
    const edges: [number, number][] = [];

    for (let i = 0; i < numNodes; i++) {
      const xi = this.getNodeVector(nodeFeatures, i);
      const distances: { j: number; dist: number }[] = [];

      for (let j = 0; j < numNodes; j++) {
        if (i === j) continue;
        const xj = this.getNodeVector(nodeFeatures, j);
        const dist = this.euclideanDistance(xi, xj);
        distances.push({ j, dist });
      }

      // Select k-nearest
      distances.sort((a, b) => a.dist - b.dist);
      for (let k = 0; k < Math.min(this.config.k!, distances.length); k++) {
        edges.push([i, distances[k].j]);
      }
    }

    return SparseMatrix.fromEdges(edges, numNodes);
  }

  private aggregate(features: Float32Array[]): Float32Array {
    if (features.length === 0) {
      return new Float32Array(this.config.outputDim);
    }

    switch (this.config.aggregation) {
      case 'max':
        return this.elementwiseMax(features);
      case 'mean':
        return this.elementwiseMean(features);
      case 'sum':
        return this.elementwiseSum(features);
    }
  }
}
```

---

## Data Structures

### Node Embeddings

```typescript
// v3/@claude-flow/gnn/src/data/node-embeddings.ts

export interface NodeEmbedding {
  id: string;
  type: NodeType;
  features: Float32Array;
  metadata: Record<string, unknown>;
}

export type NodeType =
  | 'file'
  | 'module'
  | 'class'
  | 'function'
  | 'variable'
  | 'agent'
  | 'task'
  | 'pattern';

export interface NodeEmbeddingStore {
  /**
   * Store node embedding with automatic HNSW indexing
   */
  store(embedding: NodeEmbedding): Promise<void>;

  /**
   * Batch store for efficiency
   */
  storeBatch(embeddings: NodeEmbedding[]): Promise<void>;

  /**
   * Retrieve by ID
   */
  get(id: string): Promise<NodeEmbedding | null>;

  /**
   * Get embeddings for multiple nodes
   */
  getBatch(ids: string[]): Promise<Map<string, NodeEmbedding>>;

  /**
   * Similarity search using HNSW
   */
  search(
    query: Float32Array,
    k: number,
    filter?: NodeFilter
  ): Promise<SearchResult[]>;

  /**
   * Update embedding (for incremental learning)
   */
  update(id: string, features: Float32Array): Promise<void>;
}

export interface NodeFilter {
  types?: NodeType[];
  metadata?: Record<string, unknown>;
}

export class HNSWNodeEmbeddingStore implements NodeEmbeddingStore {
  private hnsw: HNSWIndex;
  private metadata: Map<string, NodeEmbedding>;

  constructor(config: { dim: number; maxElements: number }) {
    this.hnsw = new HNSWIndex({
      dim: config.dim,
      maxElements: config.maxElements,
      efConstruction: 200,
      M: 16
    });
    this.metadata = new Map();
  }

  // Implementation...
}
```

### Edge Features

```typescript
// v3/@claude-flow/gnn/src/data/edge-features.ts

export interface EdgeFeature {
  source: string;
  target: string;
  type: EdgeType;
  features: Float32Array;
  weight?: number;
  metadata?: Record<string, unknown>;
}

export type EdgeType =
  // Code relationships
  | 'imports'
  | 'exports'
  | 'extends'
  | 'implements'
  | 'calls'
  | 'references'
  | 'depends_on'
  | 'composes'
  // Agent relationships
  | 'delegates_to'
  | 'reports_to'
  | 'communicates_with'
  | 'shares_memory'
  // Pattern relationships
  | 'similar_to'
  | 'derived_from'
  | 'supersedes';

export interface EdgeTypeEncoder {
  /**
   * Encode edge type as learnable embedding
   */
  encode(type: EdgeType): Float32Array;

  /**
   * Get all type embeddings
   */
  getAllEmbeddings(): Map<EdgeType, Float32Array>;

  /**
   * Update type embedding (learned)
   */
  update(type: EdgeType, gradient: Float32Array): void;
}

export class LearnedEdgeTypeEncoder implements EdgeTypeEncoder {
  private embeddings: Map<EdgeType, Float32Array>;
  private embeddingDim: number;

  constructor(embeddingDim: number = 32) {
    this.embeddingDim = embeddingDim;
    this.initializeEmbeddings();
  }

  private initializeEmbeddings(): void {
    const types: EdgeType[] = [
      'imports', 'exports', 'extends', 'implements', 'calls',
      'references', 'depends_on', 'composes', 'delegates_to',
      'reports_to', 'communicates_with', 'shares_memory',
      'similar_to', 'derived_from', 'supersedes'
    ];

    this.embeddings = new Map();
    for (const type of types) {
      // Xavier initialization
      const embedding = new Float32Array(this.embeddingDim);
      const scale = Math.sqrt(2.0 / this.embeddingDim);
      for (let i = 0; i < this.embeddingDim; i++) {
        embedding[i] = (Math.random() * 2 - 1) * scale;
      }
      this.embeddings.set(type, embedding);
    }
  }

  encode(type: EdgeType): Float32Array {
    return this.embeddings.get(type) ?? new Float32Array(this.embeddingDim);
  }
}
```

### Graph-Level Representations

```typescript
// v3/@claude-flow/gnn/src/data/graph-representation.ts

export interface GraphData {
  id: string;
  nodes: NodeEmbedding[];
  edges: EdgeFeature[];
  globalFeatures?: Float32Array;
}

export interface GraphEmbedding {
  id: string;
  embedding: Float32Array;
  nodeCount: number;
  edgeCount: number;
  metadata: GraphMetadata;
}

export interface GraphMetadata {
  type: GraphType;
  createdAt: number;
  updatedAt: number;
  version: string;
  statistics: GraphStatistics;
}

export type GraphType =
  | 'codebase'
  | 'module'
  | 'swarm_topology'
  | 'pattern_cluster'
  | 'impact_subgraph';

export interface GraphStatistics {
  nodeCount: number;
  edgeCount: number;
  avgDegree: number;
  density: number;
  diameter?: number;
  clusteringCoefficient?: number;
  connectedComponents: number;
}

/**
 * Graph pooling for computing graph-level embeddings
 */
export interface GraphPooling {
  /**
   * Aggregate node embeddings into graph embedding
   */
  pool(nodeEmbeddings: Float32Array, numNodes: number): Float32Array;
}

export class HierarchicalPooling implements GraphPooling {
  private ratio: number;  // Pooling ratio
  private gnn: GNNLayer;
  private poolingScoreNet: MLP;

  constructor(config: { ratio: number; embeddingDim: number }) {
    this.ratio = config.ratio;
    // Initialize pooling network
  }

  pool(nodeEmbeddings: Float32Array, numNodes: number): Float32Array {
    // Compute pooling scores
    const scores = this.computePoolingScores(nodeEmbeddings, numNodes);

    // Select top-k nodes
    const k = Math.ceil(numNodes * this.ratio);
    const selectedNodes = this.selectTopK(scores, k);

    // Create coarsened graph
    const coarsenedEmbeddings = this.coarsen(
      nodeEmbeddings, selectedNodes
    );

    // Recursive pooling or final aggregation
    if (k > 1) {
      return this.pool(coarsenedEmbeddings, k);
    }

    return coarsenedEmbeddings;
  }
}

export class Set2SetPooling implements GraphPooling {
  private lstm: LSTM;
  private processingSteps: number;

  constructor(config: { embeddingDim: number; processingSteps: number }) {
    this.processingSteps = config.processingSteps;
    // Initialize LSTM
  }

  pool(nodeEmbeddings: Float32Array, numNodes: number): Float32Array {
    const dim = nodeEmbeddings.length / numNodes;
    let q = new Float32Array(dim);  // Query vector

    for (let t = 0; t < this.processingSteps; t++) {
      // Attention over nodes
      const attention = this.computeAttention(q, nodeEmbeddings, numNodes);

      // Weighted sum of node embeddings
      const readout = this.weightedSum(nodeEmbeddings, attention, numNodes);

      // LSTM update
      q = this.lstm.step(readout, q);
    }

    return q;
  }
}
```

---

## Use Cases

### 1. Codebase Dependency Graphs

```typescript
// v3/@claude-flow/gnn/src/use-cases/codebase-graph.ts

export interface CodebaseGraphBuilder {
  /**
   * Build graph from codebase analysis
   */
  build(rootPath: string): Promise<GraphData>;

  /**
   * Update graph incrementally
   */
  updateIncremental(
    existingGraph: GraphData,
    changedFiles: string[]
  ): Promise<GraphData>;
}

export class CodeDependencyGraph implements CodebaseGraphBuilder {
  private astAnalyzer: ASTAnalyzer;
  private embedder: CodeEmbedder;

  async build(rootPath: string): Promise<GraphData> {
    // 1. Scan all source files
    const files = await this.scanSourceFiles(rootPath);

    // 2. Parse and extract symbols/dependencies
    const fileAnalysis = await Promise.all(
      files.map(f => this.astAnalyzer.analyze(f))
    );

    // 3. Create node embeddings
    const nodes: NodeEmbedding[] = [];
    for (const analysis of fileAnalysis) {
      // File node
      nodes.push({
        id: analysis.path,
        type: 'file',
        features: await this.embedder.embedFile(analysis),
        metadata: {
          path: analysis.path,
          language: analysis.language,
          complexity: analysis.complexity
        }
      });

      // Symbol nodes
      for (const symbol of analysis.symbols) {
        nodes.push({
          id: `${analysis.path}#${symbol.name}`,
          type: this.mapSymbolType(symbol.type),
          features: await this.embedder.embedSymbol(symbol),
          metadata: {
            file: analysis.path,
            line: symbol.line,
            exported: symbol.exported
          }
        });
      }
    }

    // 4. Create edges
    const edges = this.buildEdges(fileAnalysis);

    return { id: rootPath, nodes, edges };
  }

  private buildEdges(analyses: FileAnalysis[]): EdgeFeature[] {
    const edges: EdgeFeature[] = [];

    for (const analysis of analyses) {
      // Import edges
      for (const importPath of analysis.dependencies) {
        edges.push({
          source: analysis.path,
          target: this.resolveImport(importPath),
          type: 'imports',
          features: this.encodeImportFeatures(analysis, importPath)
        });
      }

      // Inheritance edges
      for (const cls of analysis.classes) {
        if (cls.extends) {
          edges.push({
            source: `${analysis.path}#${cls.name}`,
            target: cls.extends,
            type: 'extends',
            features: this.encodeInheritanceFeatures(cls)
          });
        }
      }

      // Call edges
      for (const call of analysis.functionCalls) {
        edges.push({
          source: `${analysis.path}#${call.caller}`,
          target: call.callee,
          type: 'calls',
          features: this.encodeCallFeatures(call)
        });
      }
    }

    return edges;
  }
}

/**
 * GNN-based impact analysis
 */
export class ImpactAnalyzer {
  private gnn: MessagePassingNetwork;
  private graphBuilder: CodeDependencyGraph;

  async analyzeImpact(
    changedFiles: string[],
    codebaseGraph: GraphData
  ): Promise<ImpactResult> {
    // 1. Initialize change signal on affected nodes
    const initialSignal = this.createChangeSignal(changedFiles, codebaseGraph);

    // 2. Propagate through MPNN
    const result = this.gnn.forward(
      initialSignal,
      codebaseGraph.edges,
      true  // Compute graph embedding
    );

    // 3. Identify high-impact nodes
    const impactScores = this.computeImpactScores(result.nodeEmbeddings);

    return {
      directlyAffected: changedFiles,
      indirectlyAffected: this.getIndirectlyAffected(impactScores),
      impactScores,
      riskLevel: this.assessRiskLevel(impactScores),
      suggestedTests: this.suggestTests(impactScores, codebaseGraph)
    };
  }
}
```

### 2. Agent Relationship Modeling

```typescript
// v3/@claude-flow/gnn/src/use-cases/agent-graph.ts

export interface AgentGraphManager {
  /**
   * Model current swarm topology as graph
   */
  buildTopologyGraph(agents: Agent[]): GraphData;

  /**
   * Optimize topology using GAT attention
   */
  optimizeTopology(
    currentGraph: GraphData,
    taskRequirements: TaskRequirements
  ): Promise<TopologyRecommendation>;

  /**
   * Learn communication patterns
   */
  learnCommunicationPatterns(
    messageHistory: Message[]
  ): Promise<CommunicationPatterns>;
}

export class GNNAgentCoordinator implements AgentGraphManager {
  private gat: GraphAttentionNetwork;
  private patternLearner: GraphSAGE;

  buildTopologyGraph(agents: Agent[]): GraphData {
    const nodes: NodeEmbedding[] = agents.map(agent => ({
      id: agent.id,
      type: 'agent',
      features: this.encodeAgentCapabilities(agent),
      metadata: {
        agentType: agent.type,
        status: agent.status,
        load: agent.currentLoad,
        capabilities: agent.capabilities
      }
    }));

    const edges: EdgeFeature[] = [];

    // Create edges based on topology
    for (const agent of agents) {
      for (const connection of agent.connections) {
        edges.push({
          source: agent.id,
          target: connection.targetId,
          type: this.mapConnectionType(connection.type),
          features: this.encodeConnectionFeatures(connection),
          weight: connection.strength
        });
      }
    }

    return { id: 'swarm-topology', nodes, edges };
  }

  async optimizeTopology(
    currentGraph: GraphData,
    taskRequirements: TaskRequirements
  ): Promise<TopologyRecommendation> {
    // 1. Encode task requirements as context
    const taskContext = this.encodeTaskRequirements(taskRequirements);

    // 2. Run GAT to learn attention patterns
    const { nodeFeatures, attentionWeights } = this.gat.forward(
      this.extractNodeFeatures(currentGraph),
      this.buildAdjacency(currentGraph),
      true  // Return attention
    );

    // 3. Analyze attention patterns
    const optimalConnections = this.analyzeAttention(attentionWeights);

    // 4. Recommend topology changes
    return {
      addConnections: optimalConnections.filter(c => !this.exists(c, currentGraph)),
      removeConnections: this.findWeakConnections(attentionWeights),
      reassignRoles: this.suggestRoleChanges(nodeFeatures, taskRequirements),
      estimatedImprovement: this.estimateImprovement(optimalConnections)
    };
  }

  async learnCommunicationPatterns(
    messageHistory: Message[]
  ): Promise<CommunicationPatterns> {
    // Build temporal graph from message history
    const temporalGraph = this.buildTemporalGraph(messageHistory);

    // Use GraphSAGE for inductive pattern learning
    const patterns = await this.patternLearner.forward(
      this.extractNodeFeatures(temporalGraph),
      this.buildAdjacency(temporalGraph)
    );

    return {
      frequentPatterns: this.extractFrequentPatterns(patterns),
      bottlenecks: this.identifyBottlenecks(patterns),
      recommendations: this.generateRecommendations(patterns)
    };
  }
}
```

### 3. Pattern Propagation in Swarms

```typescript
// v3/@claude-flow/gnn/src/use-cases/pattern-propagation.ts

export interface PatternPropagator {
  /**
   * Propagate learned pattern through swarm
   */
  propagate(
    pattern: Pattern,
    sourceAgent: string,
    swarmGraph: GraphData
  ): Promise<PropagationResult>;

  /**
   * Determine which agents should receive pattern
   */
  selectRecipients(
    pattern: Pattern,
    swarmGraph: GraphData
  ): Promise<string[]>;
}

export class GNNPatternPropagator implements PatternPropagator {
  private gcn: GraphConvolutionalNetwork;
  private relevancePredictor: MLP;

  async propagate(
    pattern: Pattern,
    sourceAgent: string,
    swarmGraph: GraphData
  ): Promise<PropagationResult> {
    // 1. Encode pattern as feature vector
    const patternEmbedding = await this.encodePattern(pattern);

    // 2. Initialize signal at source agent
    const nodeFeatures = this.initializeSignal(
      swarmGraph,
      sourceAgent,
      patternEmbedding
    );

    // 3. Propagate through GCN
    const propagatedFeatures = this.gcn.forward(
      nodeFeatures,
      this.buildAdjacency(swarmGraph)
    );

    // 4. Compute relevance scores
    const relevanceScores = this.computeRelevance(
      propagatedFeatures,
      patternEmbedding
    );

    // 5. Determine recipients above threshold
    const recipients = this.selectByThreshold(relevanceScores, 0.7);

    return {
      pattern,
      sourceAgent,
      recipients,
      relevanceScores,
      propagationPath: this.reconstructPath(swarmGraph, sourceAgent, recipients)
    };
  }

  async selectRecipients(
    pattern: Pattern,
    swarmGraph: GraphData
  ): Promise<string[]> {
    const patternEmbedding = await this.encodePattern(pattern);

    // Use GNN to find structurally similar agents
    const agentEmbeddings = this.gcn.forward(
      this.extractNodeFeatures(swarmGraph),
      this.buildAdjacency(swarmGraph)
    );

    // Predict relevance for each agent
    const relevance: { agentId: string; score: number }[] = [];
    const dim = agentEmbeddings.length / swarmGraph.nodes.length;

    for (let i = 0; i < swarmGraph.nodes.length; i++) {
      const agentEmb = this.getNodeVector(agentEmbeddings, i, dim);
      const combined = this.concat(agentEmb, patternEmbedding);
      const score = this.relevancePredictor.forward(combined)[0];

      relevance.push({
        agentId: swarmGraph.nodes[i].id,
        score
      });
    }

    // Return agents with high relevance
    return relevance
      .filter(r => r.score > 0.5)
      .sort((a, b) => b.score - a.score)
      .map(r => r.agentId);
  }
}
```

### 4. Impact Analysis for Changes

```typescript
// v3/@claude-flow/gnn/src/use-cases/impact-analysis.ts

export interface ChangeImpactAnalyzer {
  /**
   * Analyze impact of proposed changes
   */
  analyzeImpact(
    changes: CodeChange[],
    codebaseGraph: GraphData
  ): Promise<ImpactAnalysis>;

  /**
   * Predict test coverage needed
   */
  predictTestCoverage(
    changes: CodeChange[],
    codebaseGraph: GraphData
  ): Promise<TestCoverageRecommendation>;

  /**
   * Estimate risk level
   */
  estimateRisk(
    changes: CodeChange[],
    codebaseGraph: GraphData
  ): Promise<RiskAssessment>;
}

export interface ImpactAnalysis {
  directImpact: ImpactedEntity[];
  transitiveImpact: ImpactedEntity[];
  riskScore: number;
  suggestedReviewers: string[];
  testRecommendations: TestRecommendation[];
  rollbackComplexity: 'low' | 'medium' | 'high';
}

export interface ImpactedEntity {
  id: string;
  type: NodeType;
  impactScore: number;
  impactPath: string[];
  reason: string;
}

export class GNNImpactAnalyzer implements ChangeImpactAnalyzer {
  private mpnn: MessagePassingNetwork;
  private riskPredictor: MLP;

  async analyzeImpact(
    changes: CodeChange[],
    codebaseGraph: GraphData
  ): Promise<ImpactAnalysis> {
    // 1. Mark changed nodes
    const changedNodeIds = this.mapChangesToNodes(changes, codebaseGraph);

    // 2. Create change impact signal
    const impactSignal = this.createImpactSignal(
      codebaseGraph,
      changedNodeIds
    );

    // 3. Propagate through MPNN with edge-aware messaging
    const result = this.mpnn.forward(
      impactSignal,
      codebaseGraph.edges,
      true
    );

    // 4. Analyze propagation results
    const nodeScores = this.extractImpactScores(result.nodeEmbeddings);

    // 5. Classify direct vs transitive impact
    const directImpact = this.classifyDirectImpact(
      nodeScores,
      changedNodeIds,
      codebaseGraph
    );

    const transitiveImpact = this.classifyTransitiveImpact(
      nodeScores,
      changedNodeIds,
      codebaseGraph,
      result.messageHistory
    );

    // 6. Compute overall risk
    const riskScore = await this.computeRiskScore(
      directImpact,
      transitiveImpact,
      result.graphEmbedding!
    );

    return {
      directImpact,
      transitiveImpact,
      riskScore,
      suggestedReviewers: this.suggestReviewers(transitiveImpact),
      testRecommendations: this.suggestTests(directImpact, transitiveImpact),
      rollbackComplexity: this.assessRollbackComplexity(transitiveImpact)
    };
  }

  async predictTestCoverage(
    changes: CodeChange[],
    codebaseGraph: GraphData
  ): Promise<TestCoverageRecommendation> {
    const impact = await this.analyzeImpact(changes, codebaseGraph);

    // Find test nodes in graph
    const testNodes = codebaseGraph.nodes.filter(n =>
      n.metadata?.isTest === true
    );

    // Compute relevance of each test to impacted code
    const testRelevance = testNodes.map(testNode => {
      const relevance = this.computeTestRelevance(
        testNode,
        impact.directImpact,
        impact.transitiveImpact,
        codebaseGraph
      );

      return {
        testId: testNode.id,
        relevanceScore: relevance,
        coversEntities: this.findCoveredEntities(testNode, impact)
      };
    });

    // Sort by relevance
    testRelevance.sort((a, b) => b.relevanceScore - a.relevanceScore);

    return {
      requiredTests: testRelevance.filter(t => t.relevanceScore > 0.8),
      recommendedTests: testRelevance.filter(t =>
        t.relevanceScore > 0.5 && t.relevanceScore <= 0.8
      ),
      optionalTests: testRelevance.filter(t =>
        t.relevanceScore > 0.2 && t.relevanceScore <= 0.5
      ),
      missingCoverage: this.findMissingCoverage(impact, testRelevance)
    };
  }

  async estimateRisk(
    changes: CodeChange[],
    codebaseGraph: GraphData
  ): Promise<RiskAssessment> {
    const impact = await this.analyzeImpact(changes, codebaseGraph);

    // Risk factors
    const factors: RiskFactor[] = [
      {
        name: 'Scope',
        score: this.normalizeScope(impact.transitiveImpact.length),
        weight: 0.3
      },
      {
        name: 'Centrality',
        score: this.computeCentralityRisk(impact, codebaseGraph),
        weight: 0.25
      },
      {
        name: 'Complexity',
        score: this.computeComplexityRisk(changes),
        weight: 0.2
      },
      {
        name: 'Test Coverage',
        score: await this.computeCoverageRisk(changes, codebaseGraph),
        weight: 0.15
      },
      {
        name: 'Historical Issues',
        score: this.computeHistoricalRisk(impact.directImpact),
        weight: 0.1
      }
    ];

    const overallRisk = factors.reduce(
      (sum, f) => sum + f.score * f.weight, 0
    );

    return {
      overallRisk,
      riskLevel: this.classifyRiskLevel(overallRisk),
      factors,
      mitigations: this.suggestMitigations(factors),
      recommendation: this.generateRecommendation(overallRisk, factors)
    };
  }
}
```

---

## Integration Points

### 1. Memory Service Integration

```typescript
// v3/@claude-flow/gnn/src/integration/memory-integration.ts

export interface GNNMemoryIntegration {
  /**
   * Store graph embeddings in memory service
   */
  storeGraphEmbedding(
    graphId: string,
    embedding: GraphEmbedding
  ): Promise<void>;

  /**
   * Retrieve similar graphs
   */
  findSimilarGraphs(
    query: GraphData,
    k: number
  ): Promise<SimilarGraph[]>;

  /**
   * Store pattern with graph context
   */
  storePatternWithContext(
    pattern: Pattern,
    graphContext: GraphData
  ): Promise<void>;
}

export class MemoryServiceGNNAdapter implements GNNMemoryIntegration {
  private memoryService: MemoryService;
  private graphPooling: Set2SetPooling;

  constructor(memoryService: MemoryService) {
    this.memoryService = memoryService;
    this.graphPooling = new Set2SetPooling({
      embeddingDim: 256,
      processingSteps: 6
    });
  }

  async storeGraphEmbedding(
    graphId: string,
    embedding: GraphEmbedding
  ): Promise<void> {
    // Store in HNSW-indexed memory
    await this.memoryService.store({
      namespace: 'graphs',
      key: graphId,
      value: {
        embedding: Array.from(embedding.embedding),
        metadata: embedding.metadata,
        nodeCount: embedding.nodeCount,
        edgeCount: embedding.edgeCount
      },
      embedding: embedding.embedding  // For similarity search
    });
  }

  async findSimilarGraphs(
    query: GraphData,
    k: number
  ): Promise<SimilarGraph[]> {
    // Compute query graph embedding
    const nodeFeatures = this.extractNodeFeatures(query);
    const queryEmbedding = this.graphPooling.pool(
      nodeFeatures,
      query.nodes.length
    );

    // Search in memory
    const results = await this.memoryService.search({
      namespace: 'graphs',
      embedding: queryEmbedding,
      k,
      minSimilarity: 0.5
    });

    return results.map(r => ({
      graphId: r.key,
      similarity: r.similarity,
      metadata: r.value.metadata
    }));
  }

  async storePatternWithContext(
    pattern: Pattern,
    graphContext: GraphData
  ): Promise<void> {
    // Extract subgraph around pattern location
    const relevantSubgraph = this.extractRelevantSubgraph(
      graphContext,
      pattern.location
    );

    // Compute pattern embedding with graph context
    const patternEmbedding = await this.computeContextualEmbedding(
      pattern,
      relevantSubgraph
    );

    await this.memoryService.store({
      namespace: 'patterns',
      key: pattern.id,
      value: {
        pattern: pattern.serialize(),
        graphContext: {
          nodeIds: relevantSubgraph.nodes.map(n => n.id),
          structure: this.serializeStructure(relevantSubgraph)
        }
      },
      embedding: patternEmbedding
    });
  }
}
```

### 2. Plugin Dependency Graph

```typescript
// v3/@claude-flow/gnn/src/integration/plugin-graph.ts

export interface PluginDependencyAnalyzer {
  /**
   * Build plugin dependency graph
   */
  buildPluginGraph(plugins: Plugin[]): GraphData;

  /**
   * Analyze plugin compatibility
   */
  analyzeCompatibility(
    newPlugin: Plugin,
    existingGraph: GraphData
  ): Promise<CompatibilityResult>;

  /**
   * Optimize plugin load order
   */
  optimizeLoadOrder(
    plugins: Plugin[],
    graph: GraphData
  ): Promise<LoadOrder>;
}

export class GNNPluginAnalyzer implements PluginDependencyAnalyzer {
  private gat: GraphAttentionNetwork;
  private gcn: GraphConvolutionalNetwork;

  buildPluginGraph(plugins: Plugin[]): GraphData {
    const nodes: NodeEmbedding[] = plugins.map(plugin => ({
      id: plugin.id,
      type: 'module',
      features: this.encodePluginFeatures(plugin),
      metadata: {
        name: plugin.name,
        version: plugin.version,
        capabilities: plugin.capabilities,
        hooks: plugin.hooks
      }
    }));

    const edges: EdgeFeature[] = [];

    for (const plugin of plugins) {
      // Dependency edges
      for (const dep of plugin.dependencies) {
        edges.push({
          source: plugin.id,
          target: dep.pluginId,
          type: 'depends_on',
          features: this.encodeDependencyFeatures(dep),
          metadata: {
            versionConstraint: dep.versionConstraint,
            optional: dep.optional
          }
        });
      }

      // Capability provision edges
      for (const capability of plugin.provides) {
        // Find plugins that require this capability
        const consumers = plugins.filter(p =>
          p.requires.includes(capability)
        );

        for (const consumer of consumers) {
          edges.push({
            source: plugin.id,
            target: consumer.id,
            type: 'exports',
            features: this.encodeCapabilityFeatures(capability)
          });
        }
      }
    }

    return { id: 'plugin-graph', nodes, edges };
  }

  async analyzeCompatibility(
    newPlugin: Plugin,
    existingGraph: GraphData
  ): Promise<CompatibilityResult> {
    // 1. Create hypothetical graph with new plugin
    const extendedGraph = this.extendGraph(existingGraph, newPlugin);

    // 2. Embed extended graph
    const embeddings = this.gat.forward(
      this.extractNodeFeatures(extendedGraph),
      this.buildAdjacency(extendedGraph),
      true
    );

    // 3. Analyze attention patterns for conflicts
    const conflicts = this.detectConflicts(
      embeddings.attentionWeights,
      newPlugin.id,
      extendedGraph
    );

    // 4. Check dependency satisfaction
    const unsatisfied = this.checkDependencies(newPlugin, existingGraph);

    // 5. Predict integration issues
    const issues = await this.predictIssues(
      embeddings.nodeFeatures,
      newPlugin.id,
      extendedGraph
    );

    return {
      compatible: conflicts.length === 0 && unsatisfied.length === 0,
      conflicts,
      unsatisfiedDependencies: unsatisfied,
      potentialIssues: issues,
      recommendations: this.generateRecommendations(conflicts, unsatisfied)
    };
  }

  async optimizeLoadOrder(
    plugins: Plugin[],
    graph: GraphData
  ): Promise<LoadOrder> {
    // 1. Run GCN to propagate dependency signals
    const embeddings = this.gcn.forward(
      this.extractNodeFeatures(graph),
      this.buildAdjacency(graph)
    );

    // 2. Compute load priority scores
    const priorities = this.computePriorities(embeddings, graph);

    // 3. Topological sort with priority tie-breaking
    const order = this.topologicalSortWithPriority(graph, priorities);

    // 4. Identify parallelizable groups
    const groups = this.identifyParallelGroups(order, graph);

    return {
      sequential: order,
      parallel: groups,
      estimatedTime: this.estimateLoadTime(groups)
    };
  }
}
```

### 3. Swarm Topology Optimization

```typescript
// v3/@claude-flow/gnn/src/integration/swarm-optimization.ts

export interface SwarmTopologyOptimizer {
  /**
   * Analyze current topology efficiency
   */
  analyzeEfficiency(topology: SwarmTopology): Promise<EfficiencyAnalysis>;

  /**
   * Recommend topology changes
   */
  recommendChanges(
    topology: SwarmTopology,
    objectives: OptimizationObjectives
  ): Promise<TopologyChanges>;

  /**
   * Predict performance under load
   */
  predictPerformance(
    topology: SwarmTopology,
    workload: Workload
  ): Promise<PerformancePrediction>;
}

export interface OptimizationObjectives {
  latency: number;      // Weight for latency minimization
  throughput: number;   // Weight for throughput maximization
  resilience: number;   // Weight for fault tolerance
  cost: number;         // Weight for resource efficiency
}

export class GNNSwarmOptimizer implements SwarmTopologyOptimizer {
  private gcn: GraphConvolutionalNetwork;
  private gat: GraphAttentionNetwork;
  private predictor: MLP;

  async analyzeEfficiency(
    topology: SwarmTopology
  ): Promise<EfficiencyAnalysis> {
    const graph = this.topologyToGraph(topology);

    // 1. Compute structural metrics
    const structural = this.computeStructuralMetrics(graph);

    // 2. Run GCN to find bottlenecks
    const embeddings = this.gcn.forward(
      this.extractNodeFeatures(graph),
      this.buildAdjacency(graph)
    );

    // 3. Identify bottlenecks as high-centrality low-capacity nodes
    const bottlenecks = this.identifyBottlenecks(embeddings, graph);

    // 4. Find underutilized agents
    const underutilized = this.findUnderutilized(embeddings, graph);

    // 5. Compute overall efficiency score
    const efficiencyScore = this.computeEfficiencyScore(
      structural,
      bottlenecks,
      underutilized
    );

    return {
      efficiencyScore,
      structural,
      bottlenecks,
      underutilized,
      recommendations: this.generateEfficiencyRecommendations(
        bottlenecks,
        underutilized
      )
    };
  }

  async recommendChanges(
    topology: SwarmTopology,
    objectives: OptimizationObjectives
  ): Promise<TopologyChanges> {
    const graph = this.topologyToGraph(topology);

    // 1. Learn optimal attention patterns
    const { nodeFeatures, attentionWeights } = this.gat.forward(
      this.extractNodeFeatures(graph),
      this.buildAdjacency(graph),
      true
    );

    // 2. Identify optimal connections based on attention
    const optimalEdges = this.extractOptimalEdges(
      attentionWeights,
      objectives
    );

    // 3. Compare with current topology
    const currentEdges = new Set(
      graph.edges.map(e => `${e.source}-${e.target}`)
    );

    const addEdges = optimalEdges.filter(e =>
      !currentEdges.has(`${e.source}-${e.target}`)
    );

    const removeEdges = graph.edges.filter(e =>
      !optimalEdges.some(o =>
        o.source === e.source && o.target === e.target
      )
    );

    // 4. Predict impact of changes
    const predictedImprovement = await this.predictImprovement(
      graph,
      addEdges,
      removeEdges,
      objectives
    );

    return {
      addConnections: addEdges.map(e => ({
        source: e.source,
        target: e.target,
        type: this.recommendConnectionType(e, nodeFeatures)
      })),
      removeConnections: removeEdges.map(e => ({
        source: e.source,
        target: e.target
      })),
      rebalanceAgents: this.suggestRebalancing(nodeFeatures, objectives),
      predictedImprovement
    };
  }

  async predictPerformance(
    topology: SwarmTopology,
    workload: Workload
  ): Promise<PerformancePrediction> {
    const graph = this.topologyToGraph(topology);

    // 1. Encode workload as node features
    const workloadFeatures = this.encodeWorkload(workload, graph);

    // 2. Simulate message passing under load
    const mpnn = new MessagePassingNetwork({
      nodeDim: 128,
      edgeDim: 32,
      messageDim: 64,
      hiddenDim: 128,
      outputDim: 64,
      numSteps: 5,
      messageFunction: 'edge_network',
      updateFunction: 'gru',
      readoutFunction: 'set2set'
    });

    const result = mpnn.forward(
      workloadFeatures,
      graph.edges,
      true
    );

    // 3. Predict metrics from graph embedding
    const metrics = this.predictor.forward(result.graphEmbedding!);

    return {
      predictedLatency: metrics[0],
      predictedThroughput: metrics[1],
      predictedUtilization: this.extractUtilization(result.nodeEmbeddings),
      confidenceInterval: this.computeConfidence(metrics),
      bottleneckRisk: this.assessBottleneckRisk(result.messageHistory)
    };
  }
}
```

---

## Performance Considerations

### Sparse Matrix Operations

```typescript
// v3/@claude-flow/gnn/src/utils/sparse.ts

export interface SparseMatrix {
  rows: number;
  cols: number;
  nnz: number;  // Number of non-zeros

  getRow(i: number): number[];
  getValue(i: number, j: number): number;

  rowIterator(): IterableIterator<[number, number[]]>;
}

export class CSRMatrix implements SparseMatrix {
  private rowPtr: Int32Array;
  private colIdx: Int32Array;
  private values: Float32Array;
  public rows: number;
  public cols: number;
  public nnz: number;

  constructor(edges: [number, number][], numNodes: number, values?: number[]) {
    this.rows = numNodes;
    this.cols = numNodes;
    this.buildFromEdges(edges, values);
  }

  /**
   * Efficient sparse matrix-vector multiplication
   */
  matvec(x: Float32Array): Float32Array {
    const result = new Float32Array(this.rows);

    for (let i = 0; i < this.rows; i++) {
      let sum = 0;
      for (let j = this.rowPtr[i]; j < this.rowPtr[i + 1]; j++) {
        sum += this.values[j] * x[this.colIdx[j]];
      }
      result[i] = sum;
    }

    return result;
  }

  /**
   * Sparse matrix - dense matrix multiplication
   */
  matmul(X: Float32Array, dim: number): Float32Array {
    const result = new Float32Array(this.rows * dim);

    for (let i = 0; i < this.rows; i++) {
      for (let j = this.rowPtr[i]; j < this.rowPtr[i + 1]; j++) {
        const col = this.colIdx[j];
        const val = this.values[j];

        for (let d = 0; d < dim; d++) {
          result[i * dim + d] += val * X[col * dim + d];
        }
      }
    }

    return result;
  }
}
```

### Mini-Batch Processing

```typescript
// v3/@claude-flow/gnn/src/utils/batching.ts

export interface BatchedGraphData {
  batchedNodeFeatures: Float32Array;
  batchedEdges: EdgeData[];
  graphBoundaries: number[];  // Start index of each graph
  numGraphs: number;
}

export function batchGraphs(graphs: GraphData[]): BatchedGraphData {
  let totalNodes = 0;
  const boundaries: number[] = [0];
  const allEdges: EdgeData[] = [];

  // Calculate total size
  for (const graph of graphs) {
    totalNodes += graph.nodes.length;
    boundaries.push(totalNodes);
  }

  const dim = graphs[0].nodes[0].features.length;
  const batchedFeatures = new Float32Array(totalNodes * dim);

  let nodeOffset = 0;
  for (let g = 0; g < graphs.length; g++) {
    const graph = graphs[g];

    // Copy node features
    for (let n = 0; n < graph.nodes.length; n++) {
      const features = graph.nodes[n].features;
      for (let d = 0; d < dim; d++) {
        batchedFeatures[(nodeOffset + n) * dim + d] = features[d];
      }
    }

    // Offset edges
    for (const edge of graph.edges) {
      allEdges.push({
        source: edge.source + nodeOffset,
        target: edge.target + nodeOffset,
        features: edge.features
      });
    }

    nodeOffset += graph.nodes.length;
  }

  return {
    batchedNodeFeatures: batchedFeatures,
    batchedEdges: allEdges,
    graphBoundaries: boundaries,
    numGraphs: graphs.length
  };
}
```

### GPU Acceleration (Optional)

```typescript
// v3/@claude-flow/gnn/src/utils/gpu.ts

export interface GPUAccelerator {
  available: boolean;

  /**
   * Transfer data to GPU
   */
  toDevice(data: Float32Array): GPUBuffer;

  /**
   * Execute sparse matrix multiplication on GPU
   */
  sparseMatmulGPU(
    adj: SparseMatrix,
    features: GPUBuffer,
    dim: number
  ): GPUBuffer;

  /**
   * Transfer results back to CPU
   */
  toCPU(buffer: GPUBuffer): Float32Array;
}

export async function createGPUAccelerator(): Promise<GPUAccelerator | null> {
  // Check for WebGPU availability
  if (!navigator.gpu) {
    return null;
  }

  const adapter = await navigator.gpu.requestAdapter();
  if (!adapter) {
    return null;
  }

  const device = await adapter.requestDevice();

  return new WebGPUAccelerator(device);
}
```

---

## Migration Strategy

### Phase 1: Core GNN Layers (Week 1-2)
1. Implement GCN layer with sparse matrix support
2. Implement GAT layer with attention export
3. Implement GraphSAGE with neighbor sampling
4. Unit tests for all layers

### Phase 2: Data Structures (Week 2-3)
1. Node embedding store with HNSW integration
2. Edge feature encoding
3. Graph-level pooling operations
4. Sparse matrix utilities

### Phase 3: Use Cases (Week 3-4)
1. Codebase dependency graph builder
2. Agent relationship modeling
3. Impact analysis pipeline
4. Pattern propagation system

### Phase 4: Integration (Week 4-5)
1. Memory service integration
2. Plugin dependency analyzer
3. Swarm topology optimizer
4. CLI commands for GNN features

### Phase 5: Optimization (Week 5-6)
1. Mini-batch processing
2. GPU acceleration (optional)
3. Incremental learning support
4. Performance benchmarking

---

## Success Metrics

| Metric | Target | Measurement |
|--------|--------|-------------|
| Impact analysis accuracy | >90% | Compared to manual analysis |
| Dependency prediction | >85% | Precision/recall on held-out edges |
| Topology optimization | 20% latency reduction | A/B testing on swarms |
| Pattern propagation | 95% relevant recipients | Manual evaluation |
| Memory overhead | <100MB for 10K nodes | Memory profiling |
| Inference latency | <50ms for 1K nodes | Benchmarking |

---

## Risks and Mitigations

| Risk | Impact | Mitigation |
|------|--------|------------|
| Memory explosion on large graphs | High | Sparse representations, mini-batching |
| Training instability | Medium | Batch normalization, gradient clipping |
| Cold start (no training data) | Medium | Transfer learning from pre-trained models |
| GPU not available | Low | CPU fallback with optimized sparse ops |
| Over-smoothing in deep GNNs | Medium | Skip connections, layer normalization |

---

## References

1. Kipf & Welling (2017) - Semi-Supervised Classification with GCNs
2. Velickovic et al. (2018) - Graph Attention Networks
3. Hamilton et al. (2017) - Inductive Representation Learning on Large Graphs (GraphSAGE)
4. Gilmer et al. (2017) - Neural Message Passing for Quantum Chemistry (MPNN)
5. Wang et al. (2019) - Dynamic Graph CNN for Learning on Point Clouds (EdgeConv)

---

## Appendix: Type Definitions

```typescript
// v3/@claude-flow/gnn/src/types/index.ts

export type {
  GCNConfig,
  GCNLayer,
  GraphConvolutionalNetwork
} from './layers/gcn';

export type {
  GATConfig,
  AttentionWeights,
  GATOutput,
  GraphAttentionNetwork
} from './layers/gat';

export type {
  GraphSAGEConfig,
  NeighborSampler,
  SampledSubgraph,
  GraphSAGE
} from './layers/graphsage';

export type {
  MPNNConfig,
  EdgeData,
  MessagePassingResult,
  MessagePassingNetwork
} from './layers/mpnn';

export type {
  EdgeConvConfig,
  EdgeConvolution
} from './layers/edge-conv';

export type {
  NodeEmbedding,
  NodeType,
  NodeEmbeddingStore
} from './data/node-embeddings';

export type {
  EdgeFeature,
  EdgeType,
  EdgeTypeEncoder
} from './data/edge-features';

export type {
  GraphData,
  GraphEmbedding,
  GraphMetadata,
  GraphType,
  GraphStatistics,
  GraphPooling
} from './data/graph-representation';

export type {
  SparseMatrix,
  CSRMatrix
} from './utils/sparse';

export type {
  BatchedGraphData
} from './utils/batching';
```
