Search & Traversal Algorithms For Graphs

Imagine a network of cities connected by roads, or a group of friends connected on social media. These networks are examples of what we call “graphs” in computer science – structures made of points (nodes or vertices) connected by lines (edges or links). Graphs are incredibly useful for modeling relationships and connections in the real world.

But how do we navigate these networks? How do we find a path from one city to another, or see how connected different groups of friends are? This is where graph search and traversal algorithms come in. These are systematic methods for “visiting” or exploring the nodes in a graph, forming the foundation for solving many graph-related problems. Understanding these techniques is key to unlocking the power of graph structures.

Tip

If you are new to graphs, we highly recommend reading our Introduction to Graph Data Structure article first to understand the basics before diving into traversal!

Graph traversal simply means visiting all the reachable nodes in a graph in an organized way. Think of it like exploring a maze. A traversal algorithm starts at a specific node (the “source”) and systematically follows the edges to visit other nodes. The key is the order in which it explores.

You need a strategy for traversing a graph to make sure the below points are handled:

  • Completeness: Need to ensure that we eventually visit every part of the graph we can reach from our starting point.
  • Efficiency: Need to avoid visiting the same node multiple times unnecessarily, which could waste time and resources.

Graph search is closely related to traversal. Often, when we traverse a graph, we are looking for something specific – perhaps a particular node, or the shortest path to a node. The goal is often to find one specific node or path. The process usually stops once the target is found. Example: Finding the quickest route from your home to a destination on a map app.

Even when searching, the underlying mechanism is a traversal strategy. The search algorithm explores the graph systematically until it finds what it’s looking for or determines it doesn’t exist.

Common Strategies: Depth-First vs. Breadth-First

There are two primary strategies for exploring graphs:

  1. Depth-First Search (DFS): Imagine you’re in that maze again. DFS is like choosing one path and following it as deep as possible until you hit a dead end. Only then do you backtrack and try a different path from the last junction. It prioritizes depth.
  2. Breadth-First Search (BFS): Think of dropping a stone in a pond. BFS is like the ripples spreading out. Starting from a source node, it visits all its immediate neighbors first. Then, it visits all the neighbors of those neighbors, and so on, level by level. It explores broadly before going deeper.

The choice between DFS and BFS depends entirely on the problem you’re trying to solve. Some problems are better suited to the deep exploration of DFS, while others benefit from the level-by-level approach of BFS.

Why Are These Algorithms Important?

Graph traversal and search algorithms are fundamental tools in computer science with numerous applications:

  • Pathfinding: Finding routes in maps (GPS), networks, or games.
  • Connectivity: Checking if all nodes in a network are connected (e.g., ensuring a computer network is fully operational).
  • Web Crawling: Search engines use traversal to discover and index web pages.
  • Social Networks: Finding connections between people, recommending friends.
  • Solving Puzzles: Finding solutions in mazes or game states.
  • Dependency Resolution: Figuring out the order to install software packages or compile code files.

By learning how to systematically explore graphs, we gain the ability to analyze complex networks and solve a wide variety of interesting problems.

What’s Next?

Dive deeper into the world of graph exploration with these topics:

These algorithms are the starting point for many exciting topics in graph theory and beyond!