I cant understand mathematical representation of multigraph:

A multigraph G = (V,E,f) is composed of a set of vertices V, a set of edges E and a function f: E-> {{vi , vj} :

vi, v j is a member of V and vi is not equal to vj}.

Can somebody please guide me why there is definition of f and what is meant by E-> {{vi , vj}

Zulfi.