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A key concept in analyzing graphs are "traversals" over all the edges in a graph. The datastructure you use to store-nodes to traverse determines the order. A Depth-1st-Search finds the longest unvisited "path" before backtracking. A Breadth-1st-Search traverses all siblings before their connections.

You can process a node before traversing its edges ("pre-order"), after ("post-order"), or during ("in-order").

These same concepts also apply to "trees", arranges their nodes in a hierarchy.

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