Consider a graph $G = (V, E)$, where $V = \{v_1, v_2, ..., v_{100}\}$, $E = \{(v_i, v_j)|1 \le i < j \le 100\}$, and weight of the edge $(v_i, v_j)$ is $|i - j|$. The weight of minimum spanning tree of $G$ is _______.

A minimum spanning tree (MST) for a graph with $n = 100$ vertices requires $n - 1 = 99$ edges.

The edge weights are given by $w(v_i, v_j) = |i - j|$. The minimum possible edge weight between any two distinct vertices is $1$, which occurs between consecutive vertices $(v_i, v_{i+1})$ for $1 \le i \le 99$.

Selecting all 99 such edges:

forms a connected path covering all 100 vertices with no cycles, which is a valid spanning tree.

Total weight of this MST: