Graph analytics are at the heart of a broad range of applications such as drug discovery, page ranking, and recommendation systems. When graph size exceeds memory size, out-of-core graph processing is needed. For the widely used external memory graph processing systems, accessing storage becomes the bottleneck. We make the observation that nearly all graph algorithms have a dynamically varying number of active vertices that must be processed in each iteration. However, existing graph processing frameworks, such as GraphChi, load the entire graph in each iteration even if a small fraction of the graph is active. This limitation is due to the structure of the data storage used by these systems. In this work, we propose to use a compressed sparse row (CSR) based graph storage that is more amenable for selectively loading only a few active vertices in each iteration. But CSR based systems suffers from random update propagation to many target vertices. To solve this challenge, we propose to use a multi-log update mechanism that logs updates separately, rather than directly update the active edges in a graph. Our proposed multi-log system maintains a separate log per each vertex interval. This separation enables us to efficiently process each vertex interval by just loading the corresponding log. Further, while accessing SSD pages with fewer active vertex data, we reduce the read amplification due to the page granular accesses in SSD by logging the active vertex data in the current iteration and efficiently reading the log in the next iteration. Over the current state of the art out-of-core graph processing framework, our PartitionedVC improves performance by up to $17.84\times$, $1.19\times$, $1.65\times$, $1.38\times$, $3.15\times$, and $6.00\times$ for the widely used bfs, pagerank, community detection, graph coloring, maximal independent set, and random-walk applications, respectively.