Consider the tree arcs of a BFS traversal from a source node W in an unweighted, connected, undirected graph. The tree T formed by the tree arcs is a data structure for computing.

The shortest paths from the source node W to all other nodes in the graph.

Here's the step-by-step explanation:

1. Breadth-First Search (BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at a selected node (the 'source node'), then explores all of the neighbor nodes at the present depth prior to moving on to nodes at the next depth level.

2. In an unweighted, connected, undirected graph, BFS can be used to find the shortest path from the source node to all other nodes. This is because BFS explores all nodes at the current depth (or distance from the source node) before moving on to the next depth.

3. The tree T formed by the tree arcs of a BFS traversal is essentially a record of the exploration of the graph. Each node in the tree is connected to its parent node (the node from which it was first discovered), and the path from any node back to the source node is the shortest path in the graph.

4. Therefore, the tree T can be used as a data structure for computing the shortest paths from the source node W to all other nodes in the graph.