  We investigate in detail a recent model of colliding mobile agents [Phys.
Rev. Lett.~96, 088702], used as an alternative approach to construct evolving
networks of interactions formed by the collisions governed by suitable
dynamical rules. The system of mobile agents evolves towards a quasi-stationary
state which is, apart small fluctuations, well characterized by the density of
the system and the residence time of the agents. The residence time defines a
collision rate and by varying the collision rate, the system percolates at a
critical value, with the emergence of a giant cluster whose critical exponents
are the ones of two-dimensional percolation. Further, the degree and clustering
coefficient distributions and the average path length show that the network
associated with such a system presents non-trivial features which, depending on
the collision rule, enables one not only to recover the main properties of
standard networks, such as exponential, random and scale-free networks, but
also to obtain other topological structures. Namely, we show a specific example
where the obtained structure has topological features which characterize
accurately the structure and evolution of social networks in different
contexts, ranging from networks of acquaintances to networks of sexual
contacts.
