This research aims to develop a graph-based representation of building circulation as an extended version of the metric graph structure named UCN (Universal Circulation Network). There are several different methods and algorithms to represent pedestrians' indoor circulation for architectural purposes. The UCN has introduced a BIM-enabled approach to measure walking distances between different space objects using door-to-door connection network. In this paper, we focus on the extended development of the metric graph algorithm to expand its use scenarios such as measuring the exact distance of fire egress. There are two major issues we have encountered in this research and development: 1) finding the most-remote point in a given space objects to measure the distance of fire egress and 2) handling virtually subdivided space objects. This paper describes specific algorithms to resolve this problem on top of the structure of UCN. The major outcome of this development is the extended metric graph structure with the virtual space objects and the most-remote point. The implementation and demonstration depicted in this paper will show how the UCN structure can be enhanced in terms of its capability for visual representation as well as its extensibility of circulation-related analysis.