The goal of this paper is to analyse the scaling properties of childhood infectious disease time-series data. We present a scaling analysis of the distribution of epidemic sizes of measles, rubella, pertussis, and mumps outbreaks in Canada. This application provides a new approach in assessing infectious disease dynamics in a large vaccinated population. An inverse power-law (IPL) distribution function has been fit to the time series of epidemic sizes, and the results assessed against an exponential benchmark model. We have found that the rubella epidemic size distribution and that of measles in highly vaccinated periods follow an IPL. The IPL suggests the presence of a scale-invariant network for these diseases as a result of the heterogeneity of the individual contact rates. By contrast, it was found that pertussis and mumps were characterized by a uniform network of transmission of the exponential type, which suggests homogeneity in the contact rate or, more likely, boiled down heterogeneity by large intermixing in the population. We conclude that the topology of the network of infectious contacts depends on the disease type and its infection rate. It also appears that the socio-demographic structure of the population may play a part (e.g. pattern of contacts according to age) in the structuring of the topology of the network. The findings suggest that there is relevant information hidden in the variation of the common contagious disease time-series data, and that this information can have a bearing on the strategy of vaccination programs.