Sensor nodes used in typical monitoring applications of the Internet of Things (IoT) are an on-board resource (energy, memory, computational capability) constrained devices. The existing data aggregation algorithms have proven that compressed sensing (CS) is promising for energy efficient data aggregation. However, these methods compromise on at least one of energy efficiency, on-node computational complexity and recovery fidelity. In this paper, we propose a novel CS-aided low-complexity compressed data aggregation (LCCDA) method that divides the network into constrained overlapped clusters thereby offering an optimal trade-off among energy consumption, on-node computational complexity and recovery error. We show that the measurement matrix constructed from constrained overlapped clustering satisfies the restricted isometry property (RIP) that guarantees the recovery of the aggregated data. We make use of the graph Laplacian eigenbasis, that is based on the weight adjacency matrix, for finding the sparse representation of the measured data from randomly deployed networks, which enables the high fidelity recovery for aggregated data at the sink node. Through numerical experiments, we demonstrate that the proposed LCCDA method is capable of delivering the data to the sink with high recovery fidelity while achieving significant energy savings. © 2017 IEEE.