Depth First Search finds the lexicographical first path in the graph from a source vertex u to each vertex.

A graph is said to be disconnected if it is not connected, i.e. if two nodes exist in the graph such that there is no edge in between those nodes. In an undirected graph, a connected component is a set of vertices in a graph that are linked to each other by paths.

A bipartite graph is a graph whose vertices can be divided into two disjoint sets so that every edge connects two vertices from different sets (i.e. there are no edges which connect vertices from the same set).

Given an undirected graph, check whether the graph contains any cycle.

A undirected graph is said to be cyclic if there exists atleast one cycle among the vertices in the graph. If cycles are found, print all the cycles.

Given an undirected graph, find the distance between source vertex to all the other vertices in the graph.

Breadth first search is one of the basic and essential searching algorithms on graphs.