  This paper considers generalised network, intended as networks where (a) the
edges connecting the nodes are nonlinear, and (b) stochastic processes are
continuously indexed over both vertices and edges. Such topological structures
are normally represented through special classes of graphs, termed graphs with
Euclidean edges. We build generalised networks in which topology changes over
time instants. That is, vertices and edges can disappear at subsequent time
instants and edges may change in shape and length. We consider both cases of
linear or circular time. For the second case, the generalised network exhibits
a periodic structure. Our findings allow to illustrate pros and cons of each
setting. Generalised networks become semi-metric spaces whenever equipped with
a proper semi-metric. Our approach allows to build proper semi-metrics for the
temporally-evolving topological structures of the networks. Our final effort is
then devoted to guiding the reader through appropriate choice of classes of
functions that allow to build proper reproducing kernels when composed with the
temporally-evolving semi-metrics topological structures.
