A botnet (or, a network of bots) is an army of compromised machines that are often under the control and coordination of one or multiple sources or work in a peer-to-peer mode through a remote secure channel. Botnet infection modeling enables design for secure systems. This work proposes an innovative approach using the concept of graph theory-based closeness centrality seeded with deep learning to detect peer-to-peer botnet infection across nodes. Compromised networks can be quite big as botnets and malware infections utilize the ubiquitous internet to spread rapidly. Using closeness centrality as one of the major inclination factors of interacting nodes, the deep neural model is applied. The performance of the proposed method is evaluated by identifying botnet traffic with a high true positive rate (bot-infected node detection rate) and a low false-positive rate.