  An efficient structural identifiability analysis algorithm is developed in
this study for a broad range of network structures. The proposed method adopts
the Wright's path coefficient method to generate identifiability equations in
forms of symbolic polynomials, and then converts these symbolic equations to
binary matrices (called identifiability matrix). Several matrix operations are
introduced for identifiability matrix reduction with system equivalency
maintained. Based on the reduced identifiability matrices, the structural
identifiability of each parameter is determined. A number of benchmark models
are used to verify the validity of the proposed approach. Finally, the network
module for influenza A virus replication is employed as a real example to
illustrate the application of the proposed approach in practice. The proposed
approach can deal with cyclic networks with latent variables. The key advantage
is that it intentionally avoids symbolic computation and is thus highly
efficient. Also, this method is capable of determining the identifiability of
each single parameter and is thus of higher resolution in comparison with many
existing approaches. Overall, this study provides a basis for systematic
examination and refinement of graphical models of biological networks from the
identifiability point of view, and it has a significant potential to be
extended to more complex network structures or high-dimensional systems.
