Dismantling criminal networks or containing epidemics or misinformation through node removal is a well-studied problem. To evaluate the effectiveness of such efforts, one must measure the strength of the network before and after node removal. Process P1 is considered more effective than P2 if the strength of the residual network after removing k nodes via P1 is smaller than that from P2. This leads to the central question: How should network strength be measured? Existing metrics rely solely on structural properties of the graph, such as connectivity. However, in real-world scenarios, particularly in law enforcement, the perception of agents regarding network strength can differ significantly from structural assessments. These perceptions are often ignored in traditional metrics. We propose a new strength metric that integrates both structural properties and human perception. Using human subject surveys, we validate our approach against existing metrics. Our metric not only aligns more closely with human judgment but also outperforms traditional methods in identifying authoritative nodes and effectively dismantling both synthetic and real-world networks.