  Over the last few years, network science has proved to be useful in modeling
a variety of complex systems, composed of a large number of interconnected
units. The intricate pattern of interactions often allows the system to achieve
complex tasks, such as synchronization or collective motions. In this regard,
the interplay between network structure and dynamics has long been recognized
as a cornerstone of network science. Among dynamical processes, random walks
are undoubtedly among the most studied stochastic processes. While
traditionally, the random walkers are assumed to be independent, this
assumption breaks down if nodes are endowed with a finite carrying capacity, a
feature shared by many real-life systems. Recently, a class of nonlinear
diffusion processes accounting for the finite carrying capacities of the nodes
was introduced. The stationary nodes densities were shown to be nonlinearly
correlated with the nodes degrees, allowing to uncover the network structure by
performing a few measurements of the stationary density at the level of a
single arbitrary node and by solving an inverse problem. In this work, we
extend this class of nonlinear diffusion processes to the case of multigraphs,
in which links between nodes carry distinct attributes. Assuming the knowledge
of the pattern of interactions associated with one type of links, we show how
the degree distribution of the whole multigraph can be reconstructed. The
effectiveness of the reconstruction algorithm is demonstrated through
simulations on various multigraph topologies.
