## 1 Introduction  
According to the World Bank, more than 50% of the global population currently resides in urban areas, and this number is expected to increase by 1.5 times by 2045 [1]. The concentration of population, assets, and economic activities in urban areas significantly amplifies the risks associated with extreme events [2]. Critical infrastructure, defined as assets or systems that, if destroyed or disrupted, greatly affect societal well-being and effective governance [3, 4], is primarily located in urban city centers. For instance, a significant earthquake can often disrupt essential services, including electricity, water, and road availability. The impact on this critical infrastructure can lead to widespread consequences for communities and emergency response efforts [5, 6]. These disruptions in critical infrastructure can occur due to technical issues such as design flaws, operational failures, and mechanical breakdowns, as well as man-made or natural hazards [7; 8]. Therefore, it is crucial to understand population trends and the characteristics of this critical infrastructure, as well as its interconnections, to minimize potential socio-economic damages [9]. While there are numerous codes, standards, and rules in place for the construction of new critical infrastructure, historical city centers often struggle to comply with current guidelines. However, the consequences of failure in these historic centers can be more significant in terms of human and cultural losses [10]. One natural hazard that particularly affects historical city centers is urban fires. Infrastructures within old historic centers often consist of traditional materials with morphological characteristics that do not meet current comfort and safety standards. This infrastructure possesses significant fire loads, such as wooden ceilings and floors, textiles, and paintings. Additionally, installing common fire protection devices is often not feasible [11; 12]. Moreover, the lack of proper maintenance practices in these centers, combined with their frequent use for services and the presence of vulnerable groups (e.g., elderly people without financial support), exacerbates the problem. In this context, it is important to assess the vulnerability of historical city centers. This involves examining the system network and understanding the failure modes based on a predefined set of events. Vulnerability assessment is an extensively researched area, primarily within the context of risk analysis and natural hazard assessments [7; 13; 14]. In general, vulnerability is quantified using appropriate vulnerability indices that measure the negative consequences of extreme events such as floods, earthquakes, and fires [8]. For instance, some studies employ fragility curves to quantify vulnerability in various contexts, such as quantifying the seismic vulnerability of bridges [6]. Other vulnerability assessment frameworks view critical infrastructure as complex social-technological systems that are interdependent, meaning the condition of one part of the infrastructure influences others, and vice versa [7]. These assessments aim to characterize the process by which vulnerability is shaped within specific domains of the analyzed network. Numerous studies have examined vulnerabilities in different regions of Europe, considering aspects related to the expected severity of impacts, level of adaptation, and capacity for recovery [14]. These studies often incorporate features related to hazard, exposure, sensitivity, and capacity within the vulnerability assessment. However, most of these works focus on modern urban cities and specific climate hazards (e.g., heat stress or coastal and pluvial flooding), with limited research specifically addressing vulnerabilities in old historic cities [8]. To address this gap, this study introduces a correlation mapping approach aiming to facilitate the assessment of extreme events.