We are interested here in a natural generalization of term rewriting techniques to what we call drags, viz. finite, directed, ordered multigraphs. Each vertex is labeled by a function symbol, the arity of which governs the number of vertices to which it relates by an incoming edge in the graph. To this end, we develop a rich algebra of drags which generalizes the familiar term algebra and its associated rewriting capabilities. Viewing graphs as terms provides an initial building block for rewriting with such graphs, that should impact the many areas where computations take place on graphs.