  In many areas such as computational biology, finance or social sciences,
knowledge of an underlying graph explaining the interactions between agents is
of paramount importance but still challenging. Considering that these
interactions may be based on nonlinear relationships adds further complexity to
the topology inference problem. Among the latest methods that respond to this
need is a topology inference one proposed by the authors, which estimates a
possibly directed adjacency matrix in an online manner. Contrasting with
previous approaches based on linear models, the considered model is able to
explain nonlinear interactions between the agents in a network. The novelty in
the considered method is the use of a derivative-reproducing property to
enforce network sparsity, while reproducing kernels are used to model the
nonlinear interactions. The aim of this paper is to present a thorough
convergence analysis of this method. The analysis is proven to be sane both in
the mean and mean square sense. In addition, stability conditions are devised
to ensure the convergence of the analyzed method.
