Inferring network structure from secondary and tertiary infections on complex networks
Numerical experiments on the spread of infection on the three standard models of random and complex networks: Erd¨os-R´enyi (ER), Barab´asi-Albert (BA), and Watts-Strogatz (WS), to determine how the secondary R0 and tertiary R1 infections appear using different constant infection probability ρ. The number R0 of new infections arising from random introduction of one infected individual (patient zero) into an uninfected system is also known as the basic reproduction number. We utilize the number R1 of new and unique agents that are successively infected by the R0 individuals, given the same ρ-value. We show that the dependence of R1 on R0 can determine whether one is closer to, or farther from, ER-like networks. We further show that the deviation of WS and BA networks away from the ER network appears to be towards opposite directions. This basic result is used to infer the structures of real-world networks.