Graph Traversal

Explores all neighbors of the current node before moving to the next level of depth. BFS uses a queue (FIFO) data structure to manage the frontier.

• Optimal for: Finding the shortest path in an unweighted graph
• Memory profile: High, as it must store all nodes at the current level
• Use case: Traversing a taxonomy to find all direct subclasses of a concept
• Complexity: O(V + E) time, where V is vertices and E is edges

Explores as far down a single branch as possible before backtracking. DFS uses a stack (LIFO) or recursion to manage the traversal path.

• Optimal for: Topological sorting, cycle detection, and exhaustive path enumeration
• Memory profile: Low, proportional to the maximum depth of the graph
• Use case: Finding all descendant concepts in a deep medical ontology like SNOMED CT
• Risk: Can get trapped in infinite cycles without a visited set

Runs two simultaneous BFS traversals—one forward from the source node and one backward from the target node—until their frontiers meet. This dramatically reduces the search space.

• Optimal for: Finding the shortest connection path between two specific entities in a large graph
• Efficiency: Reduces effective branching factor from b^d to 2b^(d/2)
• Use case: Clinical entity linking to find the shortest semantic path between a symptom and a diagnosis
• Requirement: Must be able to traverse edges in reverse direction

A weighted graph traversal that finds the shortest path from a source node to all other nodes by greedily expanding the lowest cumulative cost path. Uses a priority queue (min-heap).

• Optimal for: Weighted knowledge graphs where edge properties represent cost, distance, or confidence
• Constraint: Cannot handle negative edge weights
• Use case: Finding the lowest-cost prior authorization pathway through a clinical guidelines graph
• Complexity: O((V + E) log V) with a binary heap implementation

Extends Dijkstra's algorithm by incorporating a heuristic function that estimates the remaining cost to the target. The heuristic guides the search toward the goal, pruning unpromising branches.

• Optimal for: Goal-directed pathfinding when a domain-specific heuristic is available
• Admissibility: Heuristic must never overestimate the true cost to guarantee optimality
• Use case: Navigating a FHIR resource graph to find the most relevant clinical document for a specific query
• Tuning: The quality of the heuristic directly determines performance gains over Dijkstra

A stochastic traversal where each step moves to a randomly selected neighbor. Used extensively in node embedding algorithms like DeepWalk and node2vec to generate training corpora.

• Optimal for: Approximating global graph properties without full traversal
• Key parameter: Walk length and number of walks per node control the bias-variance tradeoff
• Use case: Generating sequences for Graph Neural Network training on large healthcare knowledge graphs
• Variant: Biased random walks (node2vec) balance breadth-first and depth-first sampling via return and in-out parameters

Breadth-first search (BFS) from a patient's active medication node identifies all potential drug-drug interactions within a specified number of hops. The algorithm traverses cytochrome P450 metabolic pathways and transporter protein relationships to flag contraindications.

• Starts from the prescribed drug node
• Expands outward level-by-level through interaction edges
• Returns all reachable interacting substances within 2-3 hops
• Weights edges by clinical severity scores

Random walk with restart (RWR) algorithms traverse protein-protein interaction networks to rank candidate genes for rare diseases. The walker starts at known disease-associated seed nodes and stochastically diffuses through the graph, returning a stationary probability distribution.

• Seeds: known pathogenic variant nodes
• Restart probability: typically 0.7 to stay local
• Output: ranked list of novel gene candidates
• Validated against ClinVar and OMIM gold standards

Depth-first search (DFS) traverses temporal treatment edges to reconstruct complete patient journeys. Starting from an initial diagnosis node, the algorithm follows next-treatment edges chronologically, identifying cohorts that match specific clinical pathway patterns.

• Traces diagnosis → procedure → medication sequences
• Handles branching at decision nodes
• Filters by temporal constraints between events
• Enables comparative effectiveness research cohorts

Multi-source BFS simultaneously expands from multiple infected patient nodes through direct-contact and location-co-occurrence edges. The traversal identifies all individuals within a configurable transmission distance for epidemiological intervention.

• Sources: all confirmed case nodes
• Edge types: physical proximity, shared equipment, same ward
• Distance threshold: configurable R0-based radius
• Returns prioritized exposure risk rankings

Subgraph isomorphism traversal matches a patient's structured clinical profile against trial inclusion-exclusion criteria encoded as graph patterns. The algorithm verifies that all required condition, lab value, and medication nodes exist with correct relationship edges.

• Patient subgraph: demographics + conditions + labs + medications
• Trial pattern: required node types and edge constraints
• Matching: exact and fuzzy subgraph matching
• Handles temporal constraints on prior treatments

Shortest-path traversal between a patient's presenting symptom nodes and candidate disease nodes computes diagnostic relevance scores. The algorithm uses Dijkstra's algorithm on a weighted graph where edge weights represent clinical association strength.

• Source nodes: observed signs and symptoms
• Target nodes: all disease entities
• Edge weights: inverse of likelihood ratios
• Returns ranked differential with path explanations