How do graph traversal algorithms visit nodes without repeating them?

In computer science, graph traversal algorithms ensure that nodes are visited without repetition by maintaining a record of visited vertices. This is typically achieved by using a data structure, such as a boolean array, a hash set, or a bitmask, to track which nodes have already been processed during the traversal.

Before visiting a node, the algorithm checks this record. If the node is marked as visited, the algorithm skips it; if it is not, the algorithm marks it as visited and proceeds to explore its neighbors. This mechanism prevents the algorithm from entering infinite loops in graphs that contain cycles and ensures that each node is processed efficiently. Common traversal strategies include:

• Breadth-First Search (BFS): Uses a queue to explore the graph layer by layer, starting from a chosen root node.
• Depth-First Search (DFS): Uses a stack (or recursion) to explore as far as possible along each branch before backtracking.

By consistently updating the "visited" status of each node, these algorithms maintain the integrity of the search process across various network structures.1