Information flow in random networks: communication between nodes and navigability

This thesis explores information flow in random networks. We discuss the act of communication between nodes of a random network, focusing in particular on the achievable information transmission rate under different scenarios. We establish lower and upper bounds on the communication rate using probabilistic techniques and geometric arguments. Finally, we address the problem of navigation in random networks: we present certain algorithmic aspects that arise in trying to find the best way to navigate efficiently through a random network.