This paper studies contractual graphs, where the formation of edges between nodes result in dyadic exchanges. Each dyadic exchange is analyzed as a contractual agreement that is implemented upon fulfilment of underlying conditions. As these dyadic exchanges proliferate, the resulting population of these exchanges creates a contractual graph. A contractual framework for graphs is especially useful in applications where AI-enabled software is employed to create or automate smart contracts between nodes. While some smart contracts may be easily created and executed, others may contain a higher level of ambiguity which may prevent their efficient implementation. Ambiguity in contractual elements is especially difficult to implement, since nodes have to efficiently sense the ambiguity and allocate appropriate amounts of computational resources to the ambiguous contractual task. This paper develops a two-node contractual model of graphs, with varying levels of ambiguity in the contracts and examines its consequences for a market where tasks of differing ambiguity are available to be completed by nodes. The central theme of this paper is that as ambiguity increases, it is difficult for nodes to efficiently commit to the contract since there is an uncertainty in the amount of resources that they have to allocate for completion of the tasks specified in the contract. Thus, while linguistic ambiguity or situational ambiguity might not be cognitively burdensome for humans, it might become expensive for nodes involved in the smart contract. The paper also shows that timing matters—the order in which nodes enter the contract is important as they proceed to sense the ambiguity in a task and then allocate appropriate resources. We propose a game-theoretic formulation to scrutinize how nodes that move first to complete a task are differently impacted than those that move second. We discuss the applications of such a contractual framework for graphs and obtain conditions under which two-node contracts can achieve a successful coalition.