This paper presents a distributed algorithm for constructing the minimum-weight spanning tree (MST) in a connected undirected graph with distinct edge weights. Each node in the graph initially knows only the weights of its adjacent edges and follows the same algorithm, exchanging messages with neighbors until the MST is constructed. The total number of messages required is at most \(5N \log_2 N + 2E\), where \(N\) is the number of nodes and \(E\) is the number of edges. Messages contain at most one edge weight plus \(\log_2 8N\) bits. The algorithm can be initiated spontaneously at any node or subset of nodes. The paper also discusses the extension of the algorithm to graphs with non-distinct edge weights and the communication complexity and timing analysis of the algorithm.This paper presents a distributed algorithm for constructing the minimum-weight spanning tree (MST) in a connected undirected graph with distinct edge weights. Each node in the graph initially knows only the weights of its adjacent edges and follows the same algorithm, exchanging messages with neighbors until the MST is constructed. The total number of messages required is at most \(5N \log_2 N + 2E\), where \(N\) is the number of nodes and \(E\) is the number of edges. Messages contain at most one edge weight plus \(\log_2 8N\) bits. The algorithm can be initiated spontaneously at any node or subset of nodes. The paper also discusses the extension of the algorithm to graphs with non-distinct edge weights and the communication complexity and timing analysis of the algorithm.