This work deals with the use of the Network Robustness Simulator (NRS) to assess and compare the robustness of a set of networks. The NRS is able to compute a number of graph metrics which are put together in a single value $R^*$ by using the principal component analysis and generating heat maps as a visual result. The main features of the attack models are explained as main tool to analyze the robustness in a dynamic way.

Currently NRS implements random, targeted, epidemic and cascade failures. The main characteristics of these models are addressed.

Network controllability and its robustness has been widely studied. However, analytical methods to calculate network controllability with respect to node removals are currently lacking. We develop methods, based upon generating functions for the in- and out-degree distributions, to approximate the minimum number of driver nodes needed to control directed networks, during random and targeted node removals. By validating the proposed methods on synthetic and real-world networks, we show that our methods work very well in the case of random node removals and reasonably well in the case of targeted node removals, in particular for moderate fractions of attacked nodes.

During the talk a brief technical explanation about how the Network Robustness Simulator (NRS) has been implemented is introduced. Then a demonstration is done, showing how the NRS automatically executes a set of simulations and how the visualizer is able to deal with both single network and in interdependent networks backgrounds.

Autonomous Fifth Generation (5G) and Beyond 5G (B5G) networks require modelling tools to predict the impact on the performance when new configurations and features are applied in the network. Modeling modern networks through traditional mathematical analysis can lead to low accuracy, while the execution time and resource usage are high in network simulators. Machine Learning (ML) algorithms, and specifically Graph Neural Networks (GNNs), are suggested as a promising alternative since they can capture complex relationships from graph-like data, predicting properties with high accuracy and low resource requirements. GNNs, a use case for predicting network KPIs, and future work will be explained in this presentation.

To be announced.

The linear relation between Kemeny's constant, a graph metric directly linked with random walks, and the effective graph resistance in a regular graph has been an incentive to calculate Kemeny's constant for various networks. In this talk we consider complete bipartite graphs, (generalized) windmill graphs and tree networks with large diameter and give exact expressions of Kemeny's constant. For non-regular graphs we propose two approximations for Kemeny's constant by adding to the effective graph resistance term a linear term related to the degree heterogeneity in the graph. These approximations are exact for complete bipartite graphs, but show some discrepancies for generalized windmill and tree graphs. However, we show that a recently obtained upper-bound for Kemeny's constant based on the pseudo inverse Laplacian gives the exact value of Kemeny's constant for generalized windmill graphs. Finally, we have evaluated Kemeny's constant, its two approximations and its upper bound, for 243 real-world networks.

We consider a discrete-time between-host model for a single epidemic outbreak of an infectious disease. According to the progression of the disease, hosts are classified in regard to the pathogen load. Specifically, we are assuming the following phases: non-infectious asymptomatic phase, \textbf{infectious asymptomatic phase} (key-feature of the model where individuals show up mild or no symptoms), infectious symptomatic phase and finally an immune phase. The system takes the form of a non-linear Markov chain assuming that transitions are based on geometric or negative-binomial probability distributions. The whole system is reduced to a single non-linear renewal equation. Moreover, after linearization, two natural definitions of the Basic Reproduction number arise: firstly as the expected secondary asymptomatic cases produced by an asymptomatic primary case, and secondly as the expected number of symptomatic individuals that a symptomatic individual will produce. We define a measure of virulence as the disease-induced mortality, provided that individuals can develop symptoms, and we assume to be correlated with a weighted average transmission rate. We have found that transmission rate is higher in the symptomatic phase, but however the accumulated number of infections is higher in the asymptomatic phase.

Large scale emergencies such as a large scale flooding or a devastating storm can severely impact Critical Infrastructures (CI). Since a subsequent disruption or even destruction of CI may increase the severity of an emergency, it is important for emergency management organizations to include an impact assessment of CI in their risk management, emergency planning, and emergency preparation.

In this presentation, I will discuss a methodology for emergency management organizations to assess the impact of CI disruptions. The methodology takes into account common cause failures affecting multiple CI concurrently, cascading effects as well as the potential disruptive impact on emergency management operations. The methodology builds on earlier CI assessment approaches at the national level and has been tested in a case study.

In 1959, Richard Feynman noted that, upon reaching the nanoscale, several scaling issues would arise and require the engineering community to totally rethink the way in which nanodevices and nanocomponents were conceived. One of these ways is to deliver drugs or sensoring potencial damaged or infected areas of the body by using nanomachines (nanorobots) operating in the circulatory system (i.e. in the blood).

By interconnecting nanorobots and forming nanonetworks, their capacities are expected to be enhanced as the ensuing information exchange will allow them to cooperate towards a common goal. Nanonetworks are expected to expand the capabilities of single nanomachines, in terms of both complexity and range of operation, by allowing them to coordinate, share and fuse information.

In this work the connectivity properties of a cohort of nanorobots in the blood flux are presented. A simple model of the vessels as cylinders is used. Different simulations are carried out getting initial results for both: omnidirectional (THz) and directional (optical) wireless communications. The study also includes scenarios with different ranges and number of operating nanorobots.

The effective graph resistance is often used as a robustness metric for flow networks. Contrary to considering only the shortest path between nodes, the graph resistance captures all paths between any pair of nodes. We intend to use tthe graph resistance to improve the graph's robustness by adding k extra links to the graph. Finding the optimal solution using brute-force methods is infeasible and often greedy algorithms are used instead. If the graph resistance satisfies the so-called submodularity condition, there is a guaranteed quality of the greedy algorithm. We will show that the graph resistance does not satisfy the submodularity condition, not even in weak form.

In this talk, we will present an improved version of our well-known Network Robustness Simulator (NRS), rebranded as Network Research Simulator (NRS2). It focuses not only on network robustness but also on any other experiment based on computations over networks. We will illustrate its usefulness with an example of an AI computation to evaluate network robustness instantly.

Determining a set of "important" nodes in a network constitutes a basic endeavour in network science. Inspired by electrical flows in a resistor network, we study the diagonal element $Q_{jj}^{\dagger}$ of the pseudo-inverse matrix $Q^{\dagger}$ of the weighted Laplacian matrix of the graph $G$. We propose a new graph metric that complements the effective graph resistance $R_{G}$ and that specifies the heterogeneity of the nodal spreading capacity in a graph. We also highlight an exact relation between "structure" and "function" of a network, based on the effective resistance matrix of a graph.