  Recent studies revealed an important interplay between the detailed structure
of fibration symmetric circuits and the functionality of biological and
non-biological networks within which they have be identified. The presence of
these circuits in complex networks are directed related to the phenomenon of
cluster synchronization, which produces patterns of synchronized group of
nodes. Here we present a fast, and memory efficient, algorithm to identify
fibration symmetries over information-processing networks. This algorithm is
specially suitable for large and sparse networks since it has runtime of
complexity $O(M\log N)$ and requires $O(M+N)$ of memory resources, where $N$
and $M$ are the number of nodes and edges in the network, respectively. We
propose a modification on the so-called refinement paradigm to identify
circuits symmetrical to information flow (i.e., fibers) by finding the coarsest
refinement partition over the network. Finally, we show that the presented
algorithm provides an optimal procedure for identifying fibers, overcoming the
current approaches used in the literature.
