Graphs are data structures which consist of a set of vertices & a set of edges which connect the vertices. A graph where the edges are directed is called directed graph. Or else, it is called an undirected graph. Graphs are represented by adjacency lists & adjacency matrices. Graphs can be utilized to represent a road network where the edges are weighted as the distance among the cities. Finding the minimum distance among single source & all other vertices is called single source shortest path problem. Dijkstra's algorithm is utilized to determine shortest path from a single source to every other vertex into a directed graph. Determining shortest path among every pair of vertices is called all pairs shortest paths problem.
A spanning tree of any graph is a tree containing only those edges of the graph that connects all vertices of the graph along with minimum cost. Kruskal's & Prim's algorithms find minimum cost spanning tree into a graph. Visiting all of the nodes in a graph systematically in some manner is called traversal. Two most common methods are depth-first & breadth-first searches.