The course is taught in English. The objective of the course is to offer an overview of the behavior and modeling techniques of complex networks that range over a wide variety of cases from the Internet, to social networks and biological systems. In particular, the course will focus on the application of complex network theory to cases related to Information and Communication Technologies. The course provides the fundamental knowledge and skills to understand and model the behavior of complex networks, i.e., networks composed of a huge number of entities interacting with each other. The course is organized in 3 main parts. 1) Theory of complex networks. The fundamental mathematical notions based on random graph theory will be presented and discussed in the first part of the course. 2) Applications. Some cases of complex networks, and the associated models, will be presented. Among cases of interest, peer-to-peer systems and social networks will be briefly discussed here. 3) Laboratory. The lab activity consists in the development of simple random graph models and their application to some case of interest.

The students will acquire the following knowledge: - Fundamentals of random graph theory: basic definitions and notions, small world property, clustering coefficient, theory of evolutionary networks. - Knowledge of peer-to-peer/social networks architectures and models. And the following abilities: - Skills to model/design complex networks and identify their fundamental properties and dominant dynamics.

Basic knowledge of probability theory and stochastic processes. Basic knowledge of programming languages and simulation techniques.

Part 1 - Theory of complex networks (32 h) - Terminology and basic definitions of graph theory - Main properties of graphs: degree distribution, distances, clustering ,etc - Basic definitions of random graph theory - Erdos-Renyi random graphs - Random graphs with general distribution of the node degree - Fundamental properties: small world property and clustering coefficient - Scale free networks - Watts-Strogartz random graphs - Theory of evolutionary networks - Preferential attachment random graphs - Epidemic processes over graphs Part 2 - Applications ( 8 h) - Models of peer-to-peer systems and architectures: retrieving information over graphs - Models of the Internet - Models of social networks Part 3 - Laboratory (20h) - Simulations of some random graphs - Models of a case study - Analysis of the system properties and sensitivity of the properties to the system parameters

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The course is organized in: i) lessons where the student are exposed to the main concepts and methodologies of networks science and theory of complex networks,; ii) computer laboratories where the students have the opportunity to familiarize with the concepts learned in class and to apply them to specific problems. Students are requested to implement some of the proposed algorithms and to perform simulations to assess the theoretical predictions.

The teaching material (papers taken from the literature, slides, lecture notes) will be made available by the class teacher on the teaching portal. Further texts; • Pastor-Satorras, R.; Vespignani, A. (2004). Evolution and Structure of the Internet. Cambridge University Press. • Durrett, R. (2006). Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press.

Modalità di esame: Prova scritta (in aula); Elaborato scritto prodotto in gruppo;

Exam: Written test; Group essay;

... The evaluation of the acquired skills will be composed of two parts. - A written exam. The exam consists in 4 theoretical questions with open answer. The duration of the written exam is of 1.5 h. Each question is evaluated through a score between 0 and 7. The main goal of the written exam is to evaluate the student's level of mastering of concepts/methodologies/results learned in class. No texts/notes can be consulted during the written exam. - A report on the activities developed in the lab. The report is evaluated with a score between -2 and 4 that is added to the score of the written exam. After the report delivery, students are called for a brief discussion on the report aimed at evaluating the students' individual contribution. Report and discussion permit to evaluate the ability of the student to apply her knowledge to the solution of specific problems. In order to pass the exam, the score of 18/30 at the written exam is required. The maximum score is 30/30 cum laude (achieved if a total of 32 points are obtained)

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.