  Knowing which individuals can be more efficient in spreading a pathogen
throughout a determinate environment is a fundamental question in disease
control. Indeed, over the last years the spread of epidemic diseases and its
relationship with the topology of the involved system have been a recurrent
topic in complex network theory, taking into account both network models and
real-world data. In this paper we explore possible correlations between the
heterogeneous spread of an epidemic disease governed by the
susceptible-infected-recovered (SIR) model, and several attributes of the
originating vertices, considering Erd\"os-R\'enyi (ER), Barab\'asi-Albert (BA)
and random geometric graphs (RGG), as well as a real case of study, the US Air
Transportation Network that comprises the US 500 busiest airports along with
inter-connections. Initially, the heterogeneity of the spreading is achieved
considering the RGG networks, in which we analytically derive an expression for
the distribution of the spreading rates among the established contacts, by
assuming that such rates decay exponentially with the distance that separates
the individuals. Such distribution is also considered for the ER and BA models,
where we observe topological effects on the correlations. In the case of the
airport network, the spreading rates are empirically defined, assumed to be
directly proportional to the seat availability. Among both the theoretical and
the real networks considered, we observe a high correlation between the total
epidemic prevalence and the degree, as well as the strength and the
accessibility of the epidemic sources. For attributes such as the betweenness
centrality and the $k$-shell index, however, the correlation depends on the
topology considered.
