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"""
Advanced graph traversal algorithms for GraphRAG.
Features:
- Multi-hop reasoning with path tracking
- PageRank for node importance
- BFS/DFS traversal strategies
- Causal chain detection
- Path explanation generation
"""
from dataclasses import dataclass, field
from typing import List, Dict, Optional, Set, Tuple, Any
from enum import Enum
import networkx as nx
from collections import defaultdict
import heapq
class TraversalStrategy(Enum):
"""Graph traversal strategies"""
BFS = "bfs" # Breadth-first for shortest paths
DFS = "dfs" # Depth-first for exhaustive search
WEIGHTED = "weighted" # Dijkstra for weighted paths
PAGERANK = "pagerank" # Importance-based traversal
@dataclass
class GraphPath:
"""A path through the knowledge graph"""
nodes: List[str]
edges: List[str]
total_weight: float
hop_count: int
path_type: str # "direct", "multi-hop", "causal"
explanation: str
@dataclass
class TraversalResult:
"""Complete traversal result"""
paths: List[GraphPath]
visited_nodes: Set[str]
node_importance: Dict[str, float]
total_hops: int
reasoning_chain: List[str]
summary: str
@dataclass
class NodeInfo:
"""Information about a graph node"""
node_id: str
node_type: str
label: str
attributes: Dict[str, Any]
importance: float
neighbors: List[str]
class EnterpriseGraphTraversal:
"""
Enterprise-grade graph traversal for knowledge graph reasoning.
Supports:
- Multi-hop path finding
- Importance-weighted traversal
- Causal chain detection
- Path explanation generation
"""
def __init__(self, graph: nx.Graph):
self.graph = graph
self._pagerank_cache = None
self._node_types_cache = None
@property
def pagerank(self) -> Dict[str, float]:
"""Lazy-computed PageRank scores"""
if self._pagerank_cache is None:
if self.graph.number_of_nodes() > 0:
self._pagerank_cache = nx.pagerank(self.graph, weight='weight')
else:
self._pagerank_cache = {}
return self._pagerank_cache
def invalidate_cache(self):
"""Invalidate cached computations"""
self._pagerank_cache = None
self._node_types_cache = None
def get_node_info(self, node_id: str) -> Optional[NodeInfo]:
"""Get detailed information about a node"""
if not self.graph.has_node(node_id):
return None
attrs = dict(self.graph.nodes[node_id])
node_type = attrs.get('type', 'unknown')
label = attrs.get('label', node_id)
importance = self.pagerank.get(node_id, 0.0)
neighbors = list(self.graph.neighbors(node_id))
return NodeInfo(
node_id=node_id,
node_type=node_type,
label=label,
attributes=attrs,
importance=importance,
neighbors=neighbors
)
def find_paths(
self,
source_entities: List[str],
target_entities: Optional[List[str]] = None,
max_hops: int = 3,
strategy: TraversalStrategy = TraversalStrategy.BFS,
max_paths: int = 10
) -> TraversalResult:
"""
Find paths between entities in the graph.
Args:
source_entities: Starting entity IDs or patterns
target_entities: Optional target entity IDs
max_hops: Maximum path length
strategy: Traversal strategy to use
max_paths: Maximum number of paths to return
Returns:
TraversalResult with found paths and metadata
"""
# Find matching source nodes
source_nodes = self._find_matching_nodes(source_entities)
if not source_nodes:
return TraversalResult(
paths=[],
visited_nodes=set(),
node_importance={},
total_hops=0,
reasoning_chain=["No matching source nodes found"],
summary="Could not find relevant entities in the knowledge graph"
)
# Find matching target nodes if specified
target_nodes = None
if target_entities:
target_nodes = self._find_matching_nodes(target_entities)
# Execute traversal based on strategy
if strategy == TraversalStrategy.BFS:
paths, visited = self._bfs_traversal(source_nodes, target_nodes, max_hops, max_paths)
elif strategy == TraversalStrategy.DFS:
paths, visited = self._dfs_traversal(source_nodes, target_nodes, max_hops, max_paths)
elif strategy == TraversalStrategy.WEIGHTED:
paths, visited = self._weighted_traversal(source_nodes, target_nodes, max_hops, max_paths)
elif strategy == TraversalStrategy.PAGERANK:
paths, visited = self._pagerank_traversal(source_nodes, max_hops, max_paths)
else:
paths, visited = self._bfs_traversal(source_nodes, target_nodes, max_hops, max_paths)
# Compute node importance for visited nodes
node_importance = {n: self.pagerank.get(n, 0.0) for n in visited}
# Generate reasoning chain
reasoning_chain = self._generate_reasoning_chain(paths)
# Generate summary
summary = self._generate_summary(paths, visited)
return TraversalResult(
paths=paths,
visited_nodes=visited,
node_importance=node_importance,
total_hops=max(p.hop_count for p in paths) if paths else 0,
reasoning_chain=reasoning_chain,
summary=summary
)
def _find_matching_nodes(self, patterns: List[str]) -> Set[str]:
"""Find nodes matching given patterns"""
matches = set()
for pattern in patterns:
pattern_lower = pattern.lower()
for node in self.graph.nodes():
node_lower = str(node).lower()
attrs = self.graph.nodes[node]
label = str(attrs.get('label', '')).lower()
# Match by ID, label, or type
if (pattern_lower in node_lower or
pattern_lower in label or
pattern_lower == attrs.get('type', '').lower()):
matches.add(node)
return matches
def _bfs_traversal(
self,
sources: Set[str],
targets: Optional[Set[str]],
max_hops: int,
max_paths: int
) -> Tuple[List[GraphPath], Set[str]]:
"""Breadth-first traversal for shortest paths"""
paths = []
visited = set()
from collections import deque
for source in sources:
if len(paths) >= max_paths:
break
queue = deque([(source, [source], [], 0)])
local_visited = {source}
while queue and len(paths) < max_paths:
current, path, edges, hops = queue.popleft()
visited.add(current)
if hops >= max_hops:
continue
for neighbor in self.graph.neighbors(current):
if neighbor not in local_visited:
local_visited.add(neighbor)
edge_data = self.graph.edges[current, neighbor]
edge_label = edge_data.get('relation', 'connected')
new_path = path + [neighbor]
new_edges = edges + [edge_label]
# Check if target reached
if targets and neighbor in targets:
paths.append(self._create_path(
new_path, new_edges, hops + 1, "direct"
))
elif not targets and hops + 1 <= max_hops:
# Explore further for discovery
paths.append(self._create_path(
new_path, new_edges, hops + 1, "exploration"
))
queue.append((neighbor, new_path, new_edges, hops + 1))
return paths[:max_paths], visited
def _dfs_traversal(
self,
sources: Set[str],
targets: Optional[Set[str]],
max_hops: int,
max_paths: int
) -> Tuple[List[GraphPath], Set[str]]:
"""Depth-first traversal for exhaustive search"""
paths = []
visited = set()
def dfs(node: str, path: List[str], edges: List[str], depth: int):
if len(paths) >= max_paths:
return
visited.add(node)
if depth >= max_hops:
return
for neighbor in self.graph.neighbors(node):
if neighbor not in path: # Avoid cycles
edge_data = self.graph.edges[node, neighbor]
edge_label = edge_data.get('relation', 'connected')
new_path = path + [neighbor]
new_edges = edges + [edge_label]
if targets and neighbor in targets:
paths.append(self._create_path(
new_path, new_edges, depth + 1, "multi-hop"
))
dfs(neighbor, new_path, new_edges, depth + 1)
for source in sources:
if len(paths) >= max_paths:
break
dfs(source, [source], [], 0)
return paths[:max_paths], visited
def _weighted_traversal(
self,
sources: Set[str],
targets: Optional[Set[str]],
max_hops: int,
max_paths: int
) -> Tuple[List[GraphPath], Set[str]]:
"""Weighted path finding using Dijkstra-like approach"""
paths = []
visited = set()
for source in sources:
if len(paths) >= max_paths:
break
if not targets:
continue
for target in targets:
if len(paths) >= max_paths:
break
try:
path = nx.shortest_path(
self.graph, source, target, weight='weight'
)
if len(path) - 1 <= max_hops:
edges = []
total_weight = 0
for i in range(len(path) - 1):
edge_data = self.graph.edges[path[i], path[i+1]]
edges.append(edge_data.get('relation', 'connected'))
total_weight += edge_data.get('weight', 1.0)
gpath = GraphPath(
nodes=path,
edges=edges,
total_weight=total_weight,
hop_count=len(path) - 1,
path_type="weighted",
explanation=self._explain_path(path, edges)
)
paths.append(gpath)
visited.update(path)
except nx.NetworkXNoPath:
pass
return paths, visited
def _pagerank_traversal(
self,
sources: Set[str],
max_hops: int,
max_paths: int
) -> Tuple[List[GraphPath], Set[str]]:
"""Traverse following high-importance nodes"""
paths = []
visited = set()
for source in sources:
if len(paths) >= max_paths:
break
current = source
path = [current]
edges = []
for _ in range(max_hops):
visited.add(current)
# Get neighbors sorted by PageRank
neighbors = list(self.graph.neighbors(current))
if not neighbors:
break
# Choose highest PageRank neighbor not in path
neighbors = [n for n in neighbors if n not in path]
if not neighbors:
break
neighbors.sort(key=lambda n: self.pagerank.get(n, 0), reverse=True)
next_node = neighbors[0]
edge_data = self.graph.edges[current, next_node]
edges.append(edge_data.get('relation', 'connected'))
path.append(next_node)
current = next_node
if len(path) > 1:
paths.append(self._create_path(
path, edges, len(path) - 1, "importance"
))
return paths, visited
def _create_path(
self,
nodes: List[str],
edges: List[str],
hop_count: int,
path_type: str
) -> GraphPath:
"""Create a GraphPath with explanation"""
# Calculate weight
total_weight = 0
for i in range(len(nodes) - 1):
if self.graph.has_edge(nodes[i], nodes[i+1]):
edge_data = self.graph.edges[nodes[i], nodes[i+1]]
total_weight += edge_data.get('weight', 1.0)
return GraphPath(
nodes=nodes,
edges=edges,
total_weight=total_weight,
hop_count=hop_count,
path_type=path_type,
explanation=self._explain_path(nodes, edges)
)
def _explain_path(self, nodes: List[str], edges: List[str]) -> str:
"""Generate human-readable explanation of a path"""
if len(nodes) < 2:
return f"Single entity: {self._get_node_label(nodes[0])}"
parts = []
for i in range(len(nodes) - 1):
src_label = self._get_node_label(nodes[i])
edge_label = edges[i] if i < len(edges) else "connected to"
dst_label = self._get_node_label(nodes[i + 1])
parts.append(f"{src_label} → [{edge_label}] → {dst_label}")
return " | ".join(parts)
def _get_node_label(self, node_id: str) -> str:
"""Get human-readable label for node"""
if self.graph.has_node(node_id):
attrs = self.graph.nodes[node_id]
label = attrs.get('label', node_id)
node_type = attrs.get('type', '')
if node_type:
return f"{label} ({node_type})"
return label
return node_id
def _generate_reasoning_chain(self, paths: List[GraphPath]) -> List[str]:
"""Generate step-by-step reasoning from paths"""
if not paths:
return ["No paths found in knowledge graph"]
chain = []
for i, path in enumerate(paths[:5]): # Top 5 paths
chain.append(f"Path {i+1}: {path.explanation}")
return chain
def _generate_summary(self, paths: List[GraphPath], visited: Set[str]) -> str:
"""Generate summary of traversal results"""
if not paths:
return "No relevant paths found in the knowledge graph."
unique_entities = len(visited)
total_paths = len(paths)
avg_hops = sum(p.hop_count for p in paths) / len(paths)
return (
f"Found {total_paths} paths connecting {unique_entities} entities. "
f"Average path length: {avg_hops:.1f} hops."
)
def get_entity_neighbors(
self,
entity: str,
max_neighbors: int = 10
) -> List[NodeInfo]:
"""Get neighbors of an entity sorted by importance"""
nodes = self._find_matching_nodes([entity])
if not nodes:
return []
neighbors = set()
for node in nodes:
neighbors.update(self.graph.neighbors(node))
# Sort by PageRank
neighbor_info = []
for n in neighbors:
info = self.get_node_info(n)
if info:
neighbor_info.append(info)
neighbor_info.sort(key=lambda x: x.importance, reverse=True)
return neighbor_info[:max_neighbors]
def detect_causal_chain(
self,
effect_entity: str,
max_causes: int = 5
) -> TraversalResult:
"""Detect potential causal relationships leading to an effect"""
# Find the effect node
effect_nodes = self._find_matching_nodes([effect_entity])
if not effect_nodes:
return TraversalResult(
paths=[],
visited_nodes=set(),
node_importance={},
total_hops=0,
reasoning_chain=["Effect entity not found"],
summary="Could not identify the effect entity"
)
# Traverse backwards to find causes
causal_paths = []
visited = set()
for effect in effect_nodes:
# Use reverse BFS to find predecessors
# In undirected graph, just find connected high-importance nodes
neighbors = self.get_entity_neighbors(effect, max_neighbors=max_causes * 2)
for neighbor in neighbors[:max_causes]:
path = GraphPath(
nodes=[neighbor.node_id, effect],
edges=["contributes_to"],
total_weight=neighbor.importance,
hop_count=1,
path_type="causal",
explanation=f"{neighbor.label} may influence {self._get_node_label(effect)}"
)
causal_paths.append(path)
visited.add(neighbor.node_id)
visited.add(effect)
return TraversalResult(
paths=causal_paths,
visited_nodes=visited,
node_importance={n: self.pagerank.get(n, 0) for n in visited},
total_hops=1,
reasoning_chain=[p.explanation for p in causal_paths],
summary=f"Identified {len(causal_paths)} potential causal factors"
)
def create_traversal(graph: nx.Graph) -> EnterpriseGraphTraversal:
"""Create a graph traversal instance"""
return EnterpriseGraphTraversal(graph)
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