Recent advances in Artificial Intelligence (AI) on the Internet of Things (IoT)-enabled network edge has realized edge intelligence in several applications such as smart agriculture, smart hospitals, and smart factories by enabling low-latency and computational efficiency. However, deploying state-of-the-art Convolutional Neural Networks (CNNs) such as VGG-16 and ResNets on resource-constrained edge devices is practically infeasible due to their large number of parameters and floating-point operations (FLOPs). Thus, the concept of network pruning as a type of model compression is gaining attention for accelerating CNNs on low-power devices. State-of-the-art pruning approaches, either structured or unstructured do not consider the different underlying nature of complexities being exhibited by convolutional layers and follow a training-pruning-retraining pipeline, which results in additional computational overhead. In this work, we propose a novel and computationally efficient pruning pipeline by exploiting the inherent layer-level complexities of CNNs. Unlike typical methods, our proposed complexity-driven algorithm selects a particular layer for filter-pruning based on its contribution to overall network complexity. We follow a procedure that directly trains the pruned model and avoids the computationally complex ranking and fine-tuning steps. Moreover, we define three modes of pruning, namely parameter-aware (PA), FLOPs-aware (FA), and memory-aware (MA), to introduce versatile compression of CNNs. Our results show the competitive performance of our approach in terms of accuracy and acceleration. Lastly, we present a trade-off between different resources and accuracy which can be helpful for developers in making the right decisions in resource-constrained IoT environments.