  Using graphs to model irregular information domains is an effective approach
to deal with some of the intricacies of contemporary (network) data. A key
aspect is how the data, represented as graph signals, depend on the topology of
the graph. Widely-used approaches assume that the observed signals can be
viewed as outputs of graph filters (i.e., polynomials of a matrix
representation of the graph) whose inputs have a particular structure. Diffused
graph signals, which correspond to an originally sparse (node-localized) signal
percolated through the graph via filtering, fall into this class. In that
context, this paper deals with the problem of jointly identifying graph filters
and separating their (sparse) input signals from a mixture of diffused graph
signals, thus generalizing to the graph signal processing framework the
classical blind demixing (blind source separation) of temporal and spatial
signals. We first consider the scenario where the supporting graphs are
different across the signals, providing a theorem for demixing feasibility
along with probabilistic bounds on successful recovery. Additionally, an
analysis of the degenerate problem of demixing with a single graph is also
presented. Numerical experiments with synthetic and real-world graphs
empirically illustrating the main theoretical findings close the paper.
