The number of twigs in a graph represents the number of edges that are not part of any cycle or loop in the graph. In other words, twigs are the edges that do not form a closed loop or circuit.

In this case, we are given a graph consisting of 5 nodes. To determine the number of twigs in the tree, we need to analyze the possible combinations of edges.

- To begin, let's consider the minimum number of edges required to connect all 5 nodes. In a tree, the minimum number of edges required to connect n nodes is n-1. Therefore, in this case, we would need 4 edges to connect all 5 nodes.

- Now, let's analyze the possible combinations of edges that could form a closed loop or circuit. In order to form a closed loop, at least 3 edges are required. If we consider any 3 edges, they will form a triangle, and no additional edges can be added without creating a cycle. Therefore, any combination of 3 edges would result in a closed loop or circuit.

- Since we have 4 edges in total and any combination of 3 edges would form a closed loop, we can conclude that there is only one remaining edge that does not form a closed loop. This remaining edge is the only twig in the tree.

Hence, the correct answer is option 'D', which states that the number of twigs in the tree is 4.