The contents of this repository pertain to the Network Dynamics and Learning course for the 2022/2023 academic year at Politecnico of Turin. The project investigates the relationships among network dynamics, epidemics, game theory, and network flow. The project adopts a multi-faceted approach, utilizing theoretical analysis, simulation, and data analysis, to comprehend the interplay among these various factors and how they impact the behavior of complex systems.
This project aims to investigate the dynamics of flow and capacity in a graph network and develop algorithms and models to optimize network performance and efficiency. Real-world applications of network flow and capacity will also be explored by studying an optimization problem conducted on the Los Angeles road network to find the shortest path and the maximum flow between two nodes. Search for the social-optimum, the Wardrop equilibrium and the construction of tolls in a way to force the user-optimum to the social-optimum A perfect matching algorithm will be developed to solve a fundamental problem in graph theory with practical applications in various domains. The algorithm will evaluate all possible pairings of nodes in a graph based on criteria such as edge weights or node attributes to output a set of node pairs forming a perfect matching.
The objective of this project is to investigate the application of Markov chains and French De Groot dynamics in the context of network graphs. The project will analyze network dynamics using the fundamental concepts of Markov chains, including transition matrices, stationary distributions, and random walks. Additionally, the French De Groot dynamic will be examined as a model of opinion dynamics in a network. This model simulates the evolution of opinions among a group of individuals who interact and influence each other's beliefs over time. The study will explore how this dynamic can be used to model opinion spread in a network and how various parameters, such as social influence strength and individual stubbornness, impact the system's dynamics. The project will employ Python, using the NumPy and NetworkX libraries to implement Markov chain and French De Groot dynamic models, and the Matplotlib library to visualize simulation results.
The project aims to simulate the pandemic that occurred in Sweden in 2009, and investigate the effectiveness of vaccination as a control measure. Two sub-sections explain the simulation of epidemics on a random graph, with and without vaccination, and the third section describes estimating the social structure of the Swedish population and disease-spread parameters. The optional part explores simulating the spread of a pandemic through a population using a random graph and estimating the optimal parameter using simulated annealing. The project will involve implementing the simulation and optimization algorithms in a programming language and analyzing the results to gain insights into the spread of the disease and the effectiveness of different control measures.
The project also explores the graph coloring technique for distributed learning in potential games, with two practical applications presented. In both applications, a set of possible states is defined, and at each time instance, a node updates its color based on a probability distribution. The learning dynamics is the same in both applications, and a Nash equilibrium is found using the algorithm presented. The project also investigates the effect of different parameter values on the learning dynamics and the quality of the potential function.