Closely mimicking the hierarchical structural topology with emerging behavioral functionalities of biological neural networks in neuromorphic devices is considered of prime importance for the realization of energy-efficient intelligent systems. However, such systems reported in literature having a network of artificial synapses possess limited structural hierarchy, and are also energy-expensive. In this article, we show a simple cost-effective process to design an artificial synaptic network (ASN) comprising hierarchical structures of isolated Al and Ag micro-nano structures developed via the utilization of desiccated crack patterns, anisotropic dewetting, and self-formation. The ASN hosting network of nanogaps structurally resembles the biological synaptic network. The strategically designed ASN, despite having multiple synaptic junctions spread across the device active area of 25×105 µm2, exhibits a threshold switching (Vth ~ 1-2 V) with an ultra-low energy requirement of ~ 1.3 fJ per synaptic event which is of the same order of biological synapse. Several configurations of the order of hierarchy in the device architecture are studied comprehensively to identify the importance of the individual metallic component in contributing to threshold switching and energy minimization. The emerging potentiation behavior of conductance (G) profile under electrical stimulation and its permanence beyond are realized over a wide current compliance range of 0.25 to 300 µA, broadly classifying the short- and long-term potentiation grounded on the characteristics of filamentary structures. The scale-free correlation of potentiation in the device hosting metallic filaments of diverse shapes and strengths, could provide an ideal platform for understanding and replicating the complex behavior of the brain for neuromorphic computing. The current device provides an ideal platform for studying the cognitive behavior of the brain; the Al islands in the ASN could be used for probing the in-situ evolution of dynamic Ag filaments under ICC and for introducing external sensory signals.