Although insertions and deletions (indels) are a common type of sequence variation, their origin and their functional consequences have not yet been fully understood. It has been known that indels preferably occur in the loop regions of the affected proteins. Moreover, it has recently been demonstrated that indels are significantly more strongly correlated with functional changes than substitutions. In sum, there is substantial evidence that indels, not substitutions, are the predominant evolutionary factor when it comes to structural changes in proteins. As a consequence it comes natural to hypothesize that sizable indels can modify protein interaction interfaces, causing a gain or loss of protein-protein interactions, thereby significantly rewiring the interaction networks. In this paper, we have analyzed this relationship in a large-scale study. We have computed all paralogous protein pairs in Saccharomyces cerevisiae (Yeast) and Drosophila melanogaster (Fruit Fly), and sorted the respective alignments according to whether they contained indels of significant lengths as per a pair Hidden Markov Model (HMM)-based framework of a recent study. We subsequently computed well known centrality measures for proteins that participated in indel alignments (indel proteins) and those that did not. We found that indel proteins indeed showed greater variation in terms of these measures. This demonstrates that indels have a significant influence when it comes to rewiring of the interaction networks due to evolution, which confirms our hypothesis. In general, this study may yield relevant insights into the functional interplay of proteins and the evolutionary dynamics behind it.