Given a weighted graph $G$ with $V$ vertices and $E$ edges, where all the weights are non-negative, and a source vertex $s$, the single-source shortest path problem consists of finding the distance from $s$ to all other vertices. In this article, I describe the problem in a weighted and unweighted graph, as well as implementations using BFS for unweighted graphs and Dijkstra's algorithm for weighted graphs using an array and a priority queue.

Graph theory has numerous applications in real life. It can be used in problems found in social networks, transportation networks, the internet, chemistry, computer science, and electrical networks, among others. In general, any problem that involves relationships between objects can be modeled as a graph.