  Edge-coloured directed graphs provide an essential structure for modelling
and analysis of complex systems arising in many scientific disciplines (e.g.
feature-oriented systems, gene regulatory networks, etc.). One of the
fundamental problems for edge-coloured graphs is the detection of strongly
connected components, or SCCs. The size of edge-coloured graphs appearing in
practice can be enormous both in the number of vertices and colours. The large
number of vertices prevents us from analysing such graphs using explicit SCC
detection algorithms, such as Tarjan's, which motivates the use of a symbolic
approach. However, the large number of colours also renders existing symbolic
SCC detection algorithms impractical. This paper proposes a novel algorithm
that symbolically computes all the monochromatic strongly connected components
of an edge-coloured graph. In the worst case, the algorithm performs $O(p \cdot
n \cdot log~n)$ symbolic steps, where $p$ is the number of colours and $n$ is
the number of vertices. We evaluate the algorithm using an experimental
implementation based on binary decision diagrams (BDDs). Specifically, we use
our implementation to explore the SCCs of a large collection of coloured graphs
(up to $2^{48}$) obtained from Boolean networks -- a modelling framework
commonly appearing in systems biology.
