For MSR Robots to successfully configure from one configuration into another, the control system must be able to visualize the current structure of the robot, which cannot be done without appropriate information about each module's docking status. Although the type of information required to visualize the structure of a MSR robot differs with the physical design of the modules, there are essential information that are commonly required, such as docking orientation and identity of neighboring modules. This paper presents a novel multi-port and multi-orientation modular robot, and a representation method that can uniquely represent the geometric structure of a group of connected modules and to analyze the number of "reconfigurable DOF" within the structure. The proposed method uses labeled planar graphs and incidence matrices to describe the docking status of the modules within the structure, which helps to effectively encode the data in computer understandable expressions. In addition to the work in configuration analysis, an innovative mechanism for detecting the orientation of each docking port is also presented.