<p>Resilience, a concept receiving increasing attention in recent literature, is a relatively new area of study in power systems, particularly for distribution grids. A key challenge concerns its quantification and the development of a single, standardized metric that can be adopted for distribution grids. While some attempts have been made to quantify resilience, they are either based on complex calculations with extensive stochastic data or limited to the specific context of the research. This paper proposes a comprehensive resilience criterion employing graph theory and centrality concepts combined with loads criticality. The proposed criterion is characterized by relatively simple calculations and moderate data requirements, making it a practical measure for both researchers and distribution grid engineers. Furthermore, the paper proposes a microgrid formation approach that integrates into the resilience metric. This metric allows for evaluating resilience strategies after high-impact, low-probability (HILP) events. To validate the efficiency of the proposed resilience metric, several scenarios involving the effect of HILP events on the IEEE 123 test grid in the presence of distributed energy resources (DERs) were simulated. The results align with logical intuition and established resilience definitions, demonstrating the effectiveness of the proposed metric.</p>