Epidemic models are applied to describe epidemic processes such as the spreading of infectious viruses, opinions and fake news on real-life or online
social networks, and to analyse the epidemic processes mathmatically. The viral state evolution is closely related to the underlying network topology. Therefore, the network topology is of vital importance to describing the viral state of each individual in a network. This master thesis focuses on the network reconstruction problem of the NIMFA approximation of the Susceptible-Infected-Susceptible (SIS) epidemic process. Given the viral state series generated by the NIMFA epidemic process, we aim to estimate the adjacency matrix A of the underlying network given that the spreading parameters are known. In this thesis, we estimate the adjacency matrix of the network from the viral states by a constrained linear least-squares formulation. Our algorithm gives an accurate estimate of the adjacency matrix provided that suciently many epidemic outbreaks are observed.