This paper is concerned with the network-theoretic properties of so-called k-nearest neighbor intelligent vehicular platoons, where each vehicle communicates with k vehicles, both in front and behind. The network-theoretic properties analyzed in this paper play major roles in quantifying the resilience and robustness of three generic distributed estimation and control algorithms against communication failures and disturbances, namely resilient distributed estimation, resilient distributed consensus, and robust network formation. Based on the results for the connectivity measures of the k-nearest neighbor platoon, we show that extending the traditional platooning topologies (which were only based on interacting with nearest neighbors) to k-nearest neighbor platoons increases the resilience of distributed estimation and control algorithms to both communication failures and disturbances.