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A tree is a specialized case of a graph. A tree is a connected graph with no circuits and no self loops.
A graph consists of 3 sets - vertices, edges and a set representing relations between vertices and edges i.e. v = (a, b, c) e = (e1, e2, E3) and x = ((a,b,e1), (b,c,e2), (a,c,e3)) represents a graph where e1 joins a and b and so on.
A circuit is alternating sequence of edges and vertices where in edges are not repeated, vertices may be and starting and ending vertices are the same e.g. a e1 b e2 c e3 a means a connected to b, b to c and c to a. This forms a loop.
A self loop is a vertex looping on to itself.
As a tree does not contain any loops and is still connected, it is also called a minimally connected graph i.e. there is just one path between any 2 vertices.
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