We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this class. the notation G(n) to denote a graph with n vertices, and we denote the number of edges of G by e(G). For X 5 V, let XG denote the subgraph induced by X, and let e(X) denote the number of edges Of AIG. For v E V, define nd(v): = {x E V: {v, x} E E}, deg(v): = Ind(v

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