Write a method, in pseudocode form, to check if a given graph is connected. (in java)

The method constructs a connected tree for given graph by adding vertices to the spanning tree. A spanning tree of an undirected connected graph is its connected acyclic subgraph (i.e., a tree) that contains all the vertices of the graph.

Step 1: We first choose a random vertex from the vertex list, to define the spanning tree.

Step 2: From among the remaining vertices in the vertex list we next select another vertex that is connected by an edge to the vertices of the spanning tree.

Step 3: Repeat step 2 until no vertex can be added to expand the spanning tree. If the vertex list is empty then the graph is connected and the resulting spanning tree will be an acyclic subgraph. If the vertex list is not empty then the graph is not connected..