How did we find the probability of a node being reached in this stochastic model of a virus propagation in scale free networks?

Question

I would like some help in understanding how was this result “ kP(k)/(N< k >)” established in the following model: On a non-directed scale-free network we want to study the propagation of a virus. One vertex, chosen randomly, is being infected. At each time step, every susceptible neighbour of an infected vertex has a probability of becoming infected itself, and each infected vertex has a probability to be removed from the system. We assume here that both probabilities (infection and removal) are the same for each vertex and its neighbours. Since a site can be reached by one of its k links its probability of being reached is kP(k)/(N< k >) where P(k) is the fraction of nodes having degree (number of links) k, N the number of nodes, and < k > = InfiniteSum_index_k_of(kP(k)) denotes the average degree of nodes in the network. Note: This is extracted from this research paper , DOI: 10.1140/epjb/e2004-00119-8