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mcp__sublinear-time-solver__pageRankmcp__sublinear-time-solver__solvemcp__sublinear-time-solver__estimateEntrymcp__sublinear-time-solver__analyzeMatrixmcp__sublinear-time-solver__pageRankmcp__sublinear-time-solver__solvemcp__sublinear-time-solver__estimateEntrymcp__sublinear-time-solver__analyzeMatrix// Compute PageRank for large web graph
const pageRankResults = await mcp__sublinear-time-solver__pageRank({
adjacency: {
rows: 1000000,
cols: 1000000,
format: "coo",
data: {
values: edgeWeights,
rowIndices: sourceNodes,
colIndices: targetNodes
}
},
damping: 0.85,
epsilon: 1e-8,
maxIterations: 1000
});
console.log("Top 10 most influential nodes:",
pageRankResults.scores.slice(0, 10));// 为大规模网页图计算PageRank
const pageRankResults = await mcp__sublinear-time-solver__pageRank({
adjacency: {
rows: 1000000,
cols: 1000000,
format: "coo",
data: {
values: edgeWeights,
rowIndices: sourceNodes,
colIndices: targetNodes
}
},
damping: 0.85,
epsilon: 1e-8,
maxIterations: 1000
});
console.log("Top 10 most influential nodes:",
pageRankResults.scores.slice(0, 10));// Compute personalized PageRank for recommendation systems
const personalizedRank = await mcp__sublinear-time-solver__pageRank({
adjacency: userItemGraph,
damping: 0.85,
epsilon: 1e-6,
personalized: userPreferenceVector,
maxIterations: 500
});
// Generate recommendations based on personalized scores
const recommendations = extractTopRecommendations(personalizedRank.scores);// 为推荐系统计算个性化PageRank
const personalizedRank = await mcp__sublinear-time-solver__pageRank({
adjacency: userItemGraph,
damping: 0.85,
epsilon: 1e-6,
personalized: userPreferenceVector,
maxIterations: 500
});
// 根据个性化分数生成推荐内容
const recommendations = extractTopRecommendations(personalizedRank.scores);// Analyze influence propagation in social networks
const influenceMatrix = await mcp__sublinear-time-solver__analyzeMatrix({
matrix: socialNetworkAdjacency,
checkDominance: false,
checkSymmetry: true,
estimateCondition: true,
computeGap: true
});
// Identify key influencers and influence patterns
const keyInfluencers = identifyInfluencers(influenceMatrix);// 分析社交网络中的影响力传播
const influenceMatrix = await mcp__sublinear-time-solver__analyzeMatrix({
matrix: socialNetworkAdjacency,
checkDominance: false,
checkSymmetry: true,
estimateCondition: true,
computeGap: true
});
// 识别关键影响者和传播模式
const keyInfluencers = identifyInfluencers(influenceMatrix);// Optimize swarm communication topology
class SwarmTopologyOptimizer {
async optimizeTopology(agents, communicationRequirements) {
// Create adjacency matrix representing agent connections
const topologyMatrix = this.createTopologyMatrix(agents);
// Compute PageRank to identify communication hubs
const hubAnalysis = await mcp__sublinear-time-solver__pageRank({
adjacency: topologyMatrix,
damping: 0.9, // Higher damping for persistent communication
epsilon: 1e-6
});
// Optimize topology based on PageRank scores
return this.optimizeConnections(hubAnalysis.scores, agents);
}
async analyzeSwarmEfficiency(currentTopology) {
// Analyze current swarm communication efficiency
const efficiency = await mcp__sublinear-time-solver__solve({
matrix: currentTopology,
vector: communicationLoads,
method: "neumann",
epsilon: 1e-8
});
return {
efficiency: efficiency.solution,
bottlenecks: this.identifyBottlenecks(efficiency),
recommendations: this.generateOptimizations(efficiency)
};
}
}// 优化集群通信拓扑
class SwarmTopologyOptimizer {
async optimizeTopology(agents, communicationRequirements) {
// 创建代表Agent连接的邻接矩阵
const topologyMatrix = this.createTopologyMatrix(agents);
// 计算PageRank以识别通信枢纽
const hubAnalysis = await mcp__sublinear-time-solver__pageRank({
adjacency: topologyMatrix,
damping: 0.9, // 更高阻尼系数用于持久通信
epsilon: 1e-6
});
// 根据PageRank分数优化拓扑
return this.optimizeConnections(hubAnalysis.scores, agents);
}
async analyzeSwarmEfficiency(currentTopology) {
// 分析当前集群的通信效率
const efficiency = await mcp__sublinear-time-solver__solve({
matrix: currentTopology,
vector: communicationLoads,
method: "neumann",
epsilon: 1e-8
});
return {
efficiency: efficiency.solution,
bottlenecks: this.identifyBottlenecks(efficiency),
recommendations: this.generateOptimizations(efficiency)
};
}
}// Deploy distributed PageRank computation
const graphSandbox = await mcp__flow-nexus__sandbox_create({
template: "python",
name: "pagerank-cluster",
env_vars: {
GRAPH_SIZE: "10000000",
CHUNK_SIZE: "100000",
DAMPING_FACTOR: "0.85"
}
});
// Execute distributed PageRank algorithm
const distributedResult = await mcp__flow-nexus__sandbox_execute({
sandbox_id: graphSandbox.id,
code: `
import numpy as np
from scipy.sparse import csr_matrix
import asyncio
async def distributed_pagerank():
# Load graph partition
graph_chunk = load_graph_partition()
# Initialize PageRank computation
local_scores = initialize_pagerank_scores()
for iteration in range(max_iterations):
# Compute local PageRank update
local_update = compute_local_pagerank(graph_chunk, local_scores)
# Synchronize with other partitions
global_scores = await synchronize_scores(local_update)
# Check convergence
if check_convergence(global_scores):
break
return global_scores
result = await distributed_pagerank()
print(f"PageRank computation completed: {len(result)} nodes")
`,
language: "python"
});// 部署分布式PageRank计算
const graphSandbox = await mcp__flow-nexus__sandbox_create({
template: "python",
name: "pagerank-cluster",
env_vars: {
GRAPH_SIZE: "10000000",
CHUNK_SIZE: "100000",
DAMPING_FACTOR: "0.85"
}
});
// 执行分布式PageRank算法
const distributedResult = await mcp__flow-nexus__sandbox_execute({
sandbox_id: graphSandbox.id,
code: `
import numpy as np
from scipy.sparse import csr_matrix
import asyncio
async def distributed_pagerank():
# 加载图分区
graph_chunk = load_graph_partition()
# 初始化PageRank计算
local_scores = initialize_pagerank_scores()
for iteration in range(max_iterations):
# 计算本地PageRank更新
local_update = compute_local_pagerank(graph_chunk, local_scores)
# 与其他分区同步分数
global_scores = await synchronize_scores(local_update)
# 检查收敛性
if check_convergence(global_scores):
break
return global_scores
result = await distributed_pagerank()
print(f"PageRank computation completed: {len(result)} nodes")
`,
language: "python"
});// Train neural networks for graph analysis
const graphNeuralNetwork = await mcp__flow-nexus__neural_train({
config: {
architecture: {
type: "gnn", // Graph Neural Network
layers: [
{ type: "graph_conv", units: 64, activation: "relu" },
{ type: "graph_pool", pool_type: "mean" },
{ type: "dense", units: 32, activation: "relu" },
{ type: "dense", units: 1, activation: "sigmoid" }
]
},
training: {
epochs: 50,
batch_size: 128,
learning_rate: 0.01,
optimizer: "adam"
}
},
tier: "medium"
});// 训练用于图分析的神经网络
const graphNeuralNetwork = await mcp__flow-nexus__neural_train({
config: {
architecture: {
type: "gnn", // Graph Neural Network
layers: [
{ type: "graph_conv", units: 64, activation: "relu" },
{ type: "graph_pool", pool_type: "mean" },
{ type: "dense", units: 32, activation: "relu" },
{ type: "dense", units: 1, activation: "sigmoid" }
]
},
training: {
epochs: 50,
batch_size: 128,
learning_rate: 0.01,
optimizer: "adam"
}
},
tier: "medium"
});