Dependency Graph allows designers to describe systems including conditional branches, loops, and complex concurrent operations, etc. Systems described in Dependency Graph can be easily translated into two-phase quasi-delay-insensitive circuits. It has, however, no capability to represent mutual exclusion functions realized by arbiters. In this paper, we first propose addition of a new type of nodes that represents mutual exclusion as an extension to the Dependency Graph. Next, we describe circuit blocks mapped from the new nodes, that consists of asynchronous arbiter and Q-elements, and redefine conflict relations that are used for enhancing performance of circuits. Finally, two examples are described.