Many real-world applications deal with data that have an underlying graph structure associated with it. To perform downstream analysis on such data, it is crucial to capture relational information of nodes over their expanded neighborhood efficiently. Herein, we focus on the problem of Collective Classification (CC) for assigning labels to unlabeled nodes. Most deep learning models for CC heavily rely on differentiable variants of Weisfeiler-Lehman (WL) kernels. However, due to current computing architectures' limitations, WL kernels and their differentiable variants are limited in their ability to capture useful relational information only over a small expanded neighborhood of a node. To address this concern, we propose the framework, I-HOP, that couples differentiable kernels with an iterative inference mechanism to scale to larger neighborhoods. I-HOP scales differentiable graph kernels to capture and summarize information from a larger neighborhood in each iteration by leveraging a historical neighborhood summary obtained in the previous iteration. This recursive nature of I-HOP provides an exponential reduction in time and space complexity over straightforward differentiable graph kernels. Additionally, we point out a limitation of WL kernels where the node’s original information is decayed exponentially with an increase in neighborhood size and provide a solution to address it. Finally, extensive evaluation across 11 datasets showcases the improved results and robustness of our proposed iterative framework, I-HOP.