This paper presents a novel technique for the kinematic analysis of exoskeleton systems, based on incidence matrices in an edge-oriented graph. Kinematic equations are generated in matrix form using a base of circuits from a cycle matroid. This set of independent equations, automatically generated due to matrix orthogonalities, allows efficient computation of system's joint velocities. The method has general applicability and can be employed for modeling complex body segments and joints as complex mechanisms with large number of links and degrees of freedom. This paper illustrates the model of a particular exoskeleton system having six links.