## 3 Related Works  
In the literature, security metrics that are proposed and related to network analysis focus especially on attack graphs: they are graphical representations of potential attack paths and the various steps an attacker might take to compromise a target system or network. They provide a visual depiction of the relationships between different vulnerabilities, system components, and attack techniques that an adversary could use to achieve their objectives. Over time, various research works exploited their potential. [PERSON] et al. [24] proposed a general framework for designing network security metrics based on AGs. In [25], [PERSON] et al. propose the Network Compromise Percentage Metric while evaluating the so-called defense-in-depth strategy using AGs. In [26], [PERSON] et al. compute a ranking of states in an AG based on the probability of attackers reaching each state during a random simulation; the PageRank algorithm is adapted for such a ranking; a key assumption made in this work is that attackers would progress along different paths in an AG in a random fashion. In this work [27] from [PERSON] et al., attack trees are replaced by attack trees with more advanced AGs and attack paths with attack scenarios. In [28], [PERSON] et al. proposed a mean time-to-compromise metric based on the predator state-space model. [PERSON] et al. [29] address several important issues in calculating such metrics including the dependencies between different attack sequences in an AG and cyclic structures in such graphs. [PERSON] et al. [30], instead, proposed Bayesian networks to quantify the chances of attacks and to develop a security mitigation and management plan as a metric. More recent works start to consider vulnerabilities inside the nodes of the graph to make more accurate calculations: [PERSON] et al. [31], instead of attempting to rank unknown vulnerabilities, propose a metric that counts how many such vulnerabilities would be required for compromising network assets: a larger count implies more security because the likelihood of having more unknown vulnerabilities available, applicable, and exploitable all at the same time will be significantly lower; [PERSON] et al. [32] presented a biodiversity-inspired metric based on the effective number of distinct resources with the idea that the larger the diversity in components, the more secure the system is because it is less probable that the same vulnerability is shared between different manufacturers; [PERSON] et al. [33] proposed metrics that consider the length and the number of attack paths resulting from the graph. An implementation of AGs very common in the literature is MulVAL [34], which is a project that since 2006 proposed an end-to-end framework and reasoning system that produces AGs by conducting multihost, multistage vulnerability analysis on a network. A recent work by [PERSON] et al. [35] that uses this tool on modern network architectures leverages MulVAL to model multiple attack techniques such as spoofing, man-in-the-middle, DDoS, and other types of attacks. Metrics that pertain to this category require a high-level view of the network in order to produce and use an AG. Moreover, many of them are resource intensive and cannot be computed on devices that must maintain a very low overhead, such as switches. A device such as a switch could implement only metrics of measure type but can still exploit the possibility of managing the data plane. The aforementioned studies all employ AGs as a means of obtaining a comprehensive overview of potential attack vectors within network environments with the intent of deriving relevant metrics from such data. Distinguishing our research from these prior works, we extend our analytical scope beyond the metrics attainable through AGs alone. Instead, we integrate these metrics with lower-level data extracted from different vantage points. Furthermore, our investigation stands apart from previous efforts in its specific emphasis on networks featuring DPP and the exploitation of its intrinsic functionalities.