This article introduces a new measure of linguistic complexity which is based on the dual nature of the linguistic sign. Complexity is analyzed as consisting of three components, namely the conceptual complexity (complexity of the signified), the formal complexity (complexity of the signifier) and the form-meaning correspondence complexity. I describe a way of plotting the form-meaning relationship on a graph with two tiers (the form tier and the meaning tier) and apply a complexity measure from graph theory (average vertex degree) to assess the complexity of such graphs. The proposed method is illustrated by estimating the complexity of full noun phrases (determiner + adjective + noun) in English, Swedish, and German. I also mention the limitations and the problems which might arise when using this method.