Network topology inference from infection statistics

• Infectious SIS process may be used to determine the network topology.
• We derive mathematical relation between link weights and infection statistics.
• We test the result on both weighted and unweighted networks.

We introduce a mathematical framework for identification of network topology, based on data collected from infectious SIS process occurring on a network. An exact expression for the weight of each network link (existing or not) as a function of infectious statistics, is obtained. An algorithm for proper implementation of the analyzed concept is suggested and the validity of the obtained result is confirmed by numerical simulations performed on a number of synthetic (computer generated) networks.