  Understanding the topological characteristics of complex networks and how
they affect navigability is one of the most important goals in science today,
as it plays a central role in various economic, biological, ecological and
social systems. Here, we apply First Passage analysis tools to investigate the
properties and characteristics of random walkers in networks with different
topology. Starting with the simplest two-dimensional square lattice, we modify
its topology incrementally by randomly reconnecting links between sites. We
characterize these networks by First Passage Time from a significant number of
random walkers without interaction, varying the departure and arrival
locations. We also apply the concept of First Passage Simultaneity, which
measures the likelihood of two walkers reaching their destination together.
These measures, together with the site occupancy statistics during the
processes, allowed to differentiate the studied networks, especially the random
networks from the scale-free networks, by their navigability. We also show that
small world features can also be highlighted with the proposed technique.
