The k-core of an information graph is a common measure of a node connectedness in diverse applications. The k-core decomposition algorithm categorizes nodes into k-shells based on their connectivity. Previous research claimed that the super-spreaders are those located on the k-core of a social graph and the nodes become of less importance as they get assigned to a k-shell away from the k-core. We aim to evaluate the influence span of the social media super-spreaders, located at the k-core, in terms of the number of k-shells that their influence can reach. We base our methodology on the observation that the k-core size is directly correlated to the graph size under certain conditions. We explain these conditions and then investigate it further on real-life meme cascades extracted from Twitter. We utilize the correlation to assess the effectiveness of the k-core nodes for influence dissemination. The results of the carried-out experiments show that the correlation exists in our studied real-life datasets. A high correlation existed between the k-core size and the sizes of the inner k-shells in all the examined datasets. However, the correlation starts to decrease in the outer k-shells. Further investigations have shown that the k-shells that were less correlated exhibited a higher presence of spam accounts.