We consider a random field {X_ij, i, j = 1, ···, n} where the random variables X_ij takes on values 1 or 0. The collection {X_ij} can be viewed as a random graph with nodes {1, ···, n} by interpreting X_ij = 1 as the existence of an arc emanating from the node i to the node j. Such a representation will enable us to study ordered and unordered graphs, being also the general representation of a random graph. In this note the probability that the graph is connected is computed under the condition that Σ_iX_ki=l for k = 1, · ··, n. This result extends Ross's recent theorems on connectivity of random graphs.