graph-dependency-resolution

---

name: graph-dependency-resolution description: Graph algorithms and dependency resolution for AI agent systems. DAG construction for action gate ordering, cycle detection in skill/rule graphs, BFS/DFS traversal, semver range resolution for version conflicts, topological sort for execution ordering, and PageRank-based rule importance scoring. Sources: dagrejs/graphlib, trekhleb/javascript-algorithms, npm/node-semver, sindresorhus/toposort, asv/pagerank. origin: yana-ai — synthesized from dagrejs/graphlib, trekhleb/javascript-algorithms, npm/node-semver, sindresorhus/toposort, asv/pagerank license: Apache-2.0 version: 1.0.0 compatibility: yana-ai >= 1.3.46

/graph-dependency-resolution

When to Use

• "Which rule/skill depends on which — what's the safe load order?"
• Cycle detection: skill A depends on B depends on A → deadlock
• Semver range conflicts: two skills require different versions of the same package
• Rank rules by reference frequency to find the most critical ones
• Find shortest path between two gates (optimal middleware chain)

Do NOT use for

• Linear ordered lists with no dependencies (just sort by priority number)
• Single-hop lookups (use a Map)

---

DAG: Directed Acyclic Graph (graphlib)

import { Graph, alg } from '@dagrejs/graphlib'

// Build the YAMTAM gate dependency graph
const gateGraph = new Graph({ directed: true, multigraph: false, compound: false })

// Nodes = gates/skills/rules
gateGraph.setNode('L0', { label: 'audit-log',         tier: 0 })
gateGraph.setNode('L1', { label: 'anti-evasion',       tier: 1 })
gateGraph.setNode('L2', { label: 'shell-sanitize',     tier: 2 })
gateGraph.setNode('L3', { label: 'network-egress',     tier: 3 })
gateGraph.setNode('tool-exec', { label: 'execute',     tier: 4 })

// Edges = "must run before"
gateGraph.setEdge('L0', 'L1')    // audit-log must be set up before anti-evasion
gateGraph.setEdge('L1', 'L2')
gateGraph.setEdge('L2', 'L3')
gateGraph.setEdge('L3', 'tool-exec')

// Cycle detection — returns [] if DAG is valid, lists cycle nodes if broken
const cycles = alg.findCycles(gateGraph)
if (cycles.length > 0) {
  throw new Error(`Dependency cycle detected: ${cycles.map(c => c.join('→')).join(', ')}`)
}

// Sources = nodes with no incoming edges (entry points)
const entryPoints = gateGraph.sources()   // ['L0']
// Sinks   = nodes with no outgoing edges (terminal nodes)
const terminals   = gateGraph.sinks()     // ['tool-exec']

// Reachability: all nodes reachable from L0
const reachable = alg.dijkstra(gateGraph, 'L0')
// reachable['tool-exec'].distance === 4

// Rule: always call alg.findCycles() before executing a gate graph — cycles = deadlock
// Rule: use gateGraph.sources() to find valid entry points, never hard-code 'L0'

---

Cycle Detection + BFS/DFS (javascript-algorithms)

// BFS — shortest path in unweighted graph (level by level)
function bfs(graph: Map<string, string[]>, start: string): Map<string, number> {
  const distances = new Map<string, number>([[start, 0]])
  const queue = [start]

  while (queue.length) {
    const node = queue.shift()!
    const neighbors = graph.get(node) ?? []

    for (const n of neighbors) {
      if (!distances.has(n)) {
        distances.set(n, distances.get(node)! + 1)
        queue.push(n)
      }
    }
  }
  return distances  // distances.get(target) = hop count from start
}

// DFS — cycle detection via visited + recursion stack
function hasCycle(graph: Map<string, string[]>): boolean {
  const visited     = new Set<string>()
   inStack     =  <>()

   ():  {
    visited.(node)
    inStack.(node)

     ( neighbor  graph.(node) ?? []) {
       (!visited.(neighbor) && (neighbor))  
       (inStack.(neighbor))    
    }

    inStack.(node)
     
  }

   ( node  graph.()) {
     (!visited.(node) && (node))  
  }
   
}


 () {
   dist =  <, >([[start, ]])
   : <{ : ; :  }> = [{ : start, :  }]

   (pq.) {
    pq.( a. - b.)
     { node, d } = pq.()!
     (d > (dist.(node) ?? )) 

     ( { to, weight }  graph.(node) ?? []) {
       newDist = d + weight
       (newDist < (dist.(to) ?? )) {
        dist.(to, newDist)
        pq.({ : to, : newDist })
      }
    }
  }
   dist
}

---

Topological Sort: Execution Order (toposort)

import toposort from 'toposort'

// Sort skills/scripts so dependencies run first
// Edge [A, B] means: A must run BEFORE B
const edges: [string, string][] = [
  ['validate-manifest',  'build-release'],
  ['run-tests',          'build-release'],
  ['lint',               'run-tests'],
  ['typecheck',          'run-tests'],
  ['install-deps',       'lint'],
  ['install-deps',       'typecheck'],
]

// toposort returns nodes in reverse dep order (last dep first)
const executionOrder = toposort(edges).reverse()
// ['install-deps', 'lint', 'typecheck', 'run-tests', 'validate-manifest', 'build-release']

// With explicit node list (for isolated nodes with no edges)
const allNodes = ['install-deps', 'lint', 'typecheck', 'run-tests', 'validate-manifest', 'build-release', 'notify']
const fullOrder = toposort.array(allNodes, edges).reverse()

// Rule: always .reverse() — toposort returns reverse topological order by default
// Rule: toposort throws 'Cyclic dependency' on cycle — catch it, report the chain
try {
  toposort(edges)
} catch (e) {
  if ((e  )..()) {
      ()
  }
}

---

Semver Range Resolution (node-semver)

import semver from 'semver'

// Check if a version satisfies a range
semver.satisfies('1.3.45', '>=1.3.0 <2.0.0')  // true
semver.satisfies('2.0.0',  '>=1.3.0 <2.0.0')  // false

// Find the best version from a list that satisfies a range
const versions = ['1.2.0', '1.3.0', '1.3.44', '2.0.0', '2.1.0']
semver.maxSatisfying(versions, '^1.3.0')   // '1.3.44'
semver.minSatisfying(versions, '^2.0.0')   // '2.0.0'

// Resolve conflicting ranges from multiple skills
function resolveConflicts(
  requirements: Array<{ skill: string; range: string }>
): string | null {
  // Find intersection: a version satisfying ALL ranges
  const intersection = requirements
    .map(r => semver.validRange(r.range))
    .filter(Boolean) as string[]

  // Try known versions against all constraints
  return semver.(
    versions,
    intersection.()  
  )
}


 v = semver.()!



semver.()?.  

---

PageRank: Rule Importance Scoring

// Power iteration PageRank — find most-referenced rules/skills
// A rule with many inbound links from other rules = high importance

function pageRank(
  graph: Map<string, string[]>,   // node → outbound neighbors
  damping   = 0.85,
  iterations = 50,
  tolerance  = 1e-6
): Map<string, number> {
  const nodes = [...graph.keys()]
  const N     = nodes.length
  let ranks   = new Map(nodes.map(n => [n, 1 / N]))

  for (let i = 0; i < iterations; i++) {
    const next = new Map<string, number>()
    let delta = 0

    for (const node of nodes) {
      // Sum contributions from all nodes pointing to this one
      let sum = 0
      for (const [src, targets] of graph) {
        if (targets.includes(node)) {
          sum += (ranks.get(src) ?? 0) / targets.
        }
      }
       newRank = ( - damping) / N + damping * sum
      next.(node, newRank)
      delta += .(newRank - (ranks.(node) ?? ))
    }

    ranks = next
     (delta < tolerance)   
  }

    ([...ranks.()].( b[] - a[]))
}


 ruleRefs =  ([
  [, [, ]],
  [,  [, ]],
  [,    []],
  [,    [, ]],
  [,          []],
])

 importance = (ruleRefs)

---

Anti-Fake-Pass Checklist

❌ No cycle check before executing dependency graph (deadlock on first cycle)
❌ DFS without inStack set (can't distinguish visited from in-current-path)
❌ toposort result not .reverse()'d (execution order is backwards)
❌ semver.satisfies() on un-validated range string (throws on malformed range)
❌ Space-joined semver ranges confused with OR union (space = AND, || = OR)
❌ PageRank without convergence check (fixed iteration on large graphs = wrong)
❌ graphlib.alg.findCycles() skipped before graph traversal (silent infinite loop)