The Best Examples of Graph Traversal Algorithms Explained for Modern Problem Solving

Real examples of graph traversal algorithms explained in everyday tech

Before touching formal definitions, it helps to see real examples of graph traversal algorithms explained through problems you already recognize.

Think about these situations:

• A mapping app finding the fastest route across a busy city.
• A social network suggesting “people you may know.”
• A package delivery system optimizing routes across a country.
• A codebase analysis tool tracing function dependencies.
• A game AI exploring a maze or open world.

All of these can be modeled as graphs: nodes (cities, users, functions, locations) connected by edges (roads, friendships, calls, paths). The different examples of graph traversal algorithms are really just different strategies for walking through these graphs to answer questions.

Let’s break down the best examples and see how each algorithm fits modern use cases.

Classic examples of graph traversal algorithms explained: DFS and BFS

Two of the best-known examples of graph traversal algorithms are depth-first search (DFS) and breadth-first search (BFS). They’re simple, but they power a surprising amount of real software.

Depth-first search (DFS): exploring as far as possible first

DFS starts at a node, follows one path as far as it can, then backtracks and tries another path. Conceptually, it’s like exploring a maze by always going forward until you hit a dead end.

Real example of DFS in practice: dependency resolution in build systems
Modern build tools (like those used in large codebases at tech companies) often rely on DFS-style traversal to resolve dependencies. Imagine each module is a node, and edges point to modules it depends on. To figure out a valid build order, you:

• Start at a top-level module.
• Recursively visit all its dependencies before “building” the module itself.
• Use DFS to perform a topological sort and detect cycles.

If you’ve ever seen a “circular dependency detected” error, somewhere under the hood there was likely a DFS-based cycle detection.

Another example: solving puzzles and mazes
Game engines and puzzle solvers often use DFS to explore every possible move sequence. In a maze, DFS will go down one path to the end, then backtrack to try alternatives. It doesn’t guarantee the shortest path, but it’s great when you want to explore the entire search space or check whether any solution exists.

Breadth-first search (BFS): exploring by layers

BFS explores a graph level by level. It starts at a node, visits all neighbors, then all neighbors of neighbors, and so on. The key property: in an unweighted graph, BFS finds the shortest path in terms of number of edges.

Real example of BFS: shortest hops in social networks
Social networks like Facebook, LinkedIn, or X (Twitter) can be modeled as graphs where users are nodes and friendships or follows are edges. BFS is a natural fit for questions like:

• What is the shortest connection chain between two users?
• Who is within 2 or 3 “degrees” of this person?

When you see “You are 3 connections away from this person,” that’s conceptually BFS. Large platforms use massively optimized variants, but the underlying idea traces back to this basic traversal.

Another example: routing on unweighted grids
Consider a simple grid-based game where each move has the same cost. BFS is a clean way to find the minimum number of steps between two cells. Many pathfinding tutorials for 2D games start with BFS on a grid because it’s easy to implement and reason about.

These two classic examples of graph traversal algorithms explained show the contrast: DFS dives deep, BFS grows outward in layers.

Weighted pathfinding: examples of graph traversal algorithms beyond BFS and DFS

Real systems rarely treat all connections as equal. Roads have different travel times, network links have different latencies, and recommendations have different strengths. That’s where weighted graph algorithms come in.

Dijkstra’s algorithm: shortest path when all weights are non-negative

Dijkstra’s algorithm is the workhorse for shortest-path problems where all edge weights are non-negative.

Real example: driving directions in navigation apps
Modern navigation systems (think Google Maps, Apple Maps, Waze) use algorithms in the Dijkstra family as a core building block. The roads form a graph, intersections are nodes, and travel times or distances are edge weights. Dijkstra’s algorithm can:

• Compute the shortest path between two locations.
• Support variants like “avoid tolls” or “avoid highways” by adjusting weights.

At large scale, companies layer heuristics and precomputation on top of Dijkstra, but the conceptual engine is still shortest-path traversal.

Another example: network routing protocols
Classic Internet routing protocols such as OSPF (Open Shortest Path First) use Dijkstra’s algorithm to compute shortest paths through a network of routers. Each router builds a map of the network and runs a Dijkstra-style traversal to decide where to forward packets. The algorithmic details are documented in networking standards maintained by organizations like the IETF, which publishes Internet standards and protocols.

A* search: shortest path with a heuristic

A* (pronounced “A-star”) is like Dijkstra with a hint: it uses a heuristic to estimate the remaining distance to the goal and prioritize promising paths.

Real example: pathfinding in games and robotics
In game development, A* is the standard for character navigation on maps. Nodes represent walkable regions or waypoints; edges represent possible moves with costs. A heuristic (often straight-line distance) guides the search toward the target.

Robotics path planning uses similar ideas, especially when navigating around obstacles in a known environment. A* tends to explore far fewer nodes than plain Dijkstra, which matters if you’re running it in real time on limited hardware.

Another example: route planning with live traffic
Modern route planners don’t just care about distance; they care about current and predicted traffic. A* can incorporate heuristics based on historical traffic patterns and live data feeds. As transportation agencies and researchers publish more open data (for example, via data.gov), smarter heuristics become possible, making traversal more efficient on real road networks.

These are some of the best examples of graph traversal algorithms explained in the context of weighted graphs: Dijkstra for correctness and A* for speed with guidance.

Structural analysis: examples include cycle detection, connectivity, and components

Traversal is not just about paths; it’s also about understanding the structure of a graph.

Detecting cycles in directed graphs

DFS is often used to detect cycles, especially in directed graphs.

Real example: detecting circular dependencies in software and data pipelines
Package managers, build systems, and data workflow tools (like Airflow-style DAG schedulers) all need to know whether a dependency graph has a cycle. A DFS-based traversal can:

• Track nodes in the current recursion stack.
• Flag a cycle if it revisits a node still on the stack.

This is how a tool can tell you, “Task A depends on B, which depends on A again.” Without this kind of graph traversal, large pipelines can end up stuck.

Finding connected components

Graph traversal can group nodes into connected components—subgraphs where every node is reachable from every other.

Real example: community detection in social or biological networks
Researchers analyzing social networks, protein interaction networks, or citation graphs often start by finding connected components. BFS or DFS can:

• Identify isolated clusters of people, proteins, or papers.
• Provide a first pass before applying heavier clustering or machine learning.

Academic courses and research groups, like those at MIT OpenCourseWare, frequently introduce connected components as a core application of traversal in algorithm classes.

Web-scale examples of graph traversal algorithms explained

Graphs are not just classroom objects; they’re baked into the infrastructure of the modern web and data science.

Web crawling as a giant BFS/DFS hybrid

Search engines treat the web as a massive directed graph where pages are nodes and hyperlinks are edges.

Real example: web crawlers exploring the internet
Early web crawlers resembled BFS: start from a set of seed URLs, fetch them, extract links, and move outward layer by layer. Modern crawlers mix BFS and DFS ideas, plus prioritization strategies, to respect robots.txt, avoid spam, and stay within resource budgets.

At heart, though, it’s still graph traversal: deciding which page (node) to visit next and how deep or wide to explore.

Recommendation and influence graphs

Streaming platforms and e-commerce sites use graphs to model relationships between users, items, and behaviors.

Real example: “Because you watched…” or “Customers also bought…”
While the final recommendation models are often machine-learning driven, many systems use graph traversal as a preprocessing step:

• Build a bipartite graph of users and items.
• Traverse from a user to items they liked, then to other users who liked the same items, then to new items.

These multi-hop traversals can be implemented with BFS-like strategies or random walks. They help generate candidate items before ranking.

Modern data and 2024–2025 trends in graph traversal

As of 2024–2025, examples of graph traversal algorithms explained in industry look a bit different from the textbook versions you see in introductory classes.

Graph databases and query languages

Graph databases like Neo4j, Amazon Neptune, and open-source systems use traversal at their core. Query languages such as Cypher or Gremlin let you express patterns like:

Find all users who are within 3 friendship hops of Alice and have purchased product X.

Under the hood, this is a variant of BFS with filtering and indexing. As organizations deal with more connected data (fraud detection, supply chains, knowledge graphs), these traversal queries are becoming part of everyday analytics.

Large-scale graph processing frameworks

Frameworks like Apache Giraph, Apache Spark’s GraphX, and other distributed systems are designed to handle graphs with billions of edges. They adapt BFS, DFS, and shortest-path algorithms to run across clusters.

For example, a company analyzing a global logistics network might:

• Use parallel BFS to compute reachability from key hubs.
• Run repeated shortest-path calculations to simulate disruptions.

The theory is the same, but the implementation focuses on partitioning the graph and minimizing communication.

AI, knowledge graphs, and traversal

Knowledge graphs—used in search engines, virtual assistants, and scientific research—are essentially labeled graphs connecting entities and facts. Traversal is used to:

• Expand queries by following related concepts.
• Support reasoning over multi-step relationships.

Organizations such as the National Institutes of Health support graph-based biomedical research, where traversal helps discover relationships between genes, diseases, and drugs. These are cutting-edge examples of graph traversal algorithms explained in a scientific context.

Choosing the right algorithm: practical examples include trade-offs

When you’re solving a problem, you don’t just want an example of a graph traversal algorithm—you want the right one.

Here’s how the earlier examples line up with common decisions:

• If you need the shortest path in an unweighted graph (fewest steps), BFS is typically your best friend.
• If you need to explore all possibilities or detect cycles in directed graphs, DFS is a natural choice.
• If edges have non-negative weights and you need exact shortest paths, Dijkstra’s algorithm is the standard.
• If you care about speed on large maps and have a good distance heuristic, A* often outperforms plain Dijkstra.
• If you’re doing structural analysis—connected components, topological sorting, cycle detection—DFS and BFS are the usual tools.

The best examples of graph traversal algorithms explained are the ones tied to a clear question: shortest path, reachability, structure, or exploration. Once you know the question, the algorithm choice becomes much easier.

FAQ: examples of graph traversal algorithms, uses, and misconceptions

What are some common examples of graph traversal algorithms used in real systems?

Common examples of graph traversal algorithms include depth-first search (DFS), breadth-first search (BFS), Dijkstra’s algorithm, A* search, and variations like bidirectional search. DFS and BFS show up in dependency analysis, social networks, and connectivity checks. Dijkstra and A* dominate routing, navigation, and pathfinding problems.

Can you give an example of graph traversal in everyday apps?

Yes. When your map app finds a route from your home to a restaurant, it is running a shortest-path traversal on a road graph. When a social network tells you that you share “15 mutual friends” with someone, it has traversed a friendship graph to count overlapping neighbors.

Are DFS and BFS still relevant in 2024–2025, or are they outdated?

They are very much alive. Even though large systems use highly optimized and distributed implementations, the core ideas of DFS and BFS are still taught in leading universities and used in production systems. They form the backbone of more advanced methods, so understanding them pays off.

How do I decide between Dijkstra’s algorithm and A* in practice?

Use Dijkstra when you need guaranteed shortest paths and don’t have a good heuristic, or when you’re computing distances from one node to many others. Use A* when you know both the start and goal and can compute a reasonable lower-bound estimate of the remaining distance (for example, straight-line distance on a map). A* often explores far fewer nodes, which matters for real-time applications.

Where can I learn more about graph algorithms from authoritative sources?

You can explore open course materials and references from trusted institutions. For example, MIT OpenCourseWare offers free algorithm courses, and many universities host lecture notes on graph algorithms. For broader data and research, the U.S. government’s data.gov portal links to datasets where graph analysis is applied in transportation, health, and science.