## 1 Introduction  
Today's information societies depend deeply on optical networks to handle massive flows of data between data centers, cloud computing platforms, telecom networks, and end users, ensuring fast and reliable information exchange. Optical networks are communication infrastructures that utilize light for transmitting, processing, and switching information, relying on optical fibers as the transmission medium [1]. Since the proposal of using optical fibers for communications purposes by [PERSON] in 1966 [2], the evolution of optical networks has been marked by many breakthroughs [3]. Among the most significant ones is the development of WDM (wavelength division multiplexing) technology. WDM can significantly increase the capacity of optical transmission by simultaneously transmitting multiple optical signals, often referred to as optical channels, through a single optical fiber, with each channel utilizing its own wavelength. Therefore, the problem of designing optical networks is markedly different from designing electrical networks in the sense that it involves, besides finding a path for each traffic demand (routing), also assigning a wavelength to that path (wavelength assignment). The routing and wavelength assignment (RWA) problem is a well-studied topic in the field of optical networking. This problem can be formulated using integer linear programming (ILP) with the objective of minimizing the number of wavelengths, leading to optimal solutions [4]. However, since the problem is NP-complete (nondeterministic polynomial-time complete), it requiresintensive computation, limiting its applicability to small and medium-sized networks. For large networks, one must rely on suboptimal heuristics to speed up the calculations. (see [5] for an overview). More recently, machine learning techniques have also been explored to obtain near-optimal RWA solutions with a significant reduction in computation time [6]. The RWA problem can be static or dynamic [5]. In static RWA, all traffic demands are known in advance, and the goal is to minimize the number of wavelengths needed to route all of them. All decisions are made offline, before any traffic is actually sent. In dynamic RWA, traffic demands arrive over time in a random way. The number of available wavelengths is fixed, and the goal is to route the demands while minimizing the blocking of requests. Decisions are made online, as the demands arrive. A drawback of dynamic RWA is that it requires a very advanced control plane, such as SDN (Software-Defined Networking), which increases the complexity and sophistication of the network. Another closely related topic that is paramount for network designers is understanding how the number of required wavelengths, also denoted wavelength usage, to accommodate a given traffic demand relates to parameters associated with network's physical topology and identifying general trends in this relationship. This problem has been the focus of many studies. To the best of our knowledge [7; 8] were the first works to study that interdependency, considering topological parameters such as node degree and its variance, physical connectivity, internodal distance, and the number of spanning trees, using statistical analysis that required the generation of large number of random networks. Furthermore, ref. [9] adds algebraic connectivity to the modelling and shows that this parameter provides the most accurate estimate of wavelength usage among those studied by the authors. Interestingly, ref. [10] also showed that algebraic connectivity is strongly correlated with other network metrics like capacity and robustness. While these studies rely on general random networks, ref. [11] addresses the wavelength usage problem but focuses on other networks models, such as small-world and scale-free networks, considering parameters like the average shortest paths length. Survivability has become a critical feature of modern optical networks, particularly in backbone segments, due to the huge volume of traffic they handle.