  In this article we investigate the topological changes undergone by
trajectory networks as a consequence of progressive geographical infiltration.
Trajectory networks, a type of knitted network, are obtained by establishing
paths between geographically distributed nodes while following an associated
vector field. For instance, the nodes could correspond to neurons along the
cortical surface and the vector field could correspond to the gradient of
neurotrophic factors, or the nodes could represent towns while the vector
fields would be given by economical and/or geographical gradients. Therefore
trajectory networks are natural models of a large number of geographical
structures. The geographical infiltrations correspond to the addition of new
local connections between nearby existing nodes. As such, these infiltrations
could be related to several real-world processes such as contaminations,
diseases, attacks, parasites, etc. The way in which progressive geographical
infiltrations affect trajectory networks is investigated in terms of the
degree, clustering coefficient, size of the largest component and the lengths
of the existing chains measured along the infiltrations. It is shown that the
maximum infiltration distance plays a critical role in the intensity of the
induced topological changes. For large enough values of this parameter, the
chains intrinsic to the trajectory networks undergo a collapse which is shown
not to be related to the percolation of the network also implied by the
infiltrations.
