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

v3/implementation/adrs/ADR-029-gnn-integration.md

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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

ChallengeCurrent LimitationGNN Solution
Dependency trackingManual traversal, no learned patternsGCN propagates dependency signals
Impact analysisStatic rules, misses indirect effectsMessage passing captures multi-hop effects
Agent coordinationFixed topologiesGAT learns optimal attention patterns
Pattern discoveryPer-file analysis onlyGraph-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

MetricTargetMeasurement
Impact analysis accuracy>90%Compared to manual analysis
Dependency prediction>85%Precision/recall on held-out edges
Topology optimization20% latency reductionA/B testing on swarms
Pattern propagation95% relevant recipientsManual evaluation
Memory overhead<100MB for 10K nodesMemory profiling
Inference latency<50ms for 1K nodesBenchmarking

Risks and Mitigations

RiskImpactMitigation
Memory explosion on large graphsHighSparse representations, mini-batching
Training instabilityMediumBatch normalization, gradient clipping
Cold start (no training data)MediumTransfer learning from pre-trained models
GPU not availableLowCPU fallback with optimized sparse ops
Over-smoothing in deep GNNsMediumSkip 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';