Analysis of Complex Networks: Theory and Applications

Politecnico di Milano
10-11-12, 17-18-19 October, 2017

Exam for PhD students


Last update: March 6, 2017

Analysis of Complex Networks:
Theory and Applications

Politecnico di Milano
10-11-12, 17-18-19 October, 2017

PhD course organised by


A network is a set of agents pairwise connected by links. Despite the simplicity of this definition, the theoretical properties of networks are extremely rich and diversified. Most notably, networks turn out to be extremely flexible in modeling a broad variety of phenomena characterized by a large number of interconnected elementary units: social networks, the Internet and the WWW, sensor networks, ecological communities, biochemical systems, energy transportation networks, economic and financial networks, are just but a few examples.


The course is part of the teaching activities organized by the PhD Program in Information Technology at Politecnico di Milano, yet it is not only addressed to PhD students, but to all researchers working in any areas of science and engineering and interested in the theory and applications of complex networks. The aim is to illustrate the fundamental theoretical notions as well as a number of applications in specific fields. The basic definitions, a few useful indicators, and the most important network models are first introduced. Then, dynamical processes evolving on top of the network will be considered, to illustrate how phenomena such as cascade failures, epidemic/information diffusion, or evolutionary games in structured populations may evolve.




Francesco Cadini, Dept. Energy, Politecnico di Milano [webpage]
Renato Casagrandi,
DEIB, Politecnico di Milano [webpage]

Fabio Dercole, DEIB, Politecnico di Milano [webpage]
Francesca Ieva, Dept. Mathematics, Politecnico di Milano [webpage]
Lorenzo Mari
, DEIB, Politecnico di Milano [webpage]
Carlo Piccardi,
, Politecnico di Milano [webpage]
Lucia Tajoli, DIG, Politecnico di Milano [webpage]



The language of the course (lectures and notes) is English.

Tuesday, October 10 
9:00 - 13:00 
Networks and their representation
Examples of real world networks. Undirected/directed, weighted/unweighed networks. Adjacency and Laplacian matrices. Bipartite networks and projections. Connected and strongly connected components.
Quantifying network properties
Distance and diameter. Clustering coefficient. Degree, strength, and degree distribution. Correlated networks.

Wednesday, October 11 
9:00 - 13:00 
Network models
Random (Erdos-Renyi) networks - Scale-free (Barabasi-Albert) networks - Small-world (Watts-Strogatz) networks
Degree, betweenness, closeness, eigenvector centralities, hub/authority scores, PageRank

Thursday, October 12 
9:00 - 11:00 
Evolutionary games on networks
Evolutionary games in finite and infinite well-mixed populations. Birth-death and imitation processes. Social dilemmas. Evolutionary games in structured populations: from regular to scale-free networks of contact. Does the locality of interactions relax the social dilemma? Should we imitate better performing neighbors in heterogeneous situations? The role of hubs in fostering cooperation.
11:00 - 13:00 
Mesoscale network analysis (I)
Community detection. Modularity. Random-walk-based methods.

Tuesday, October 17 
9:00 - 10:00 
Latent space models
Latent space definition. Inferring the latent space coordinates. Applications to clustering algorithms.
10:00 - 13:00 
Network robustness: basic tools and applications to power transmission grids
Topological level of service indicators. Robustness (resilience) to failures and attacks. Most critical components identification. Reliability-based centralities and application to optimal power grid expansion. Cascading failures. Motter-Lai model. Power flow-based models and application to power grids robustness analysis.

Wednesday, October 18 
9:00 - 13:00 
[Casagrandi and Mari] 
Epidemiological processes on networks
SIR-like processes on networks. Epidemiological thresholds. Disease control via network topology. Spatially-explicit networks. Multi-layered networks. Environmental connectivity. Human mobility using big-data (mobile-phone traces).

Thursday, October 19 
9:00 - 11:00 
Mesoscale network analysis (II)
Core-periphery analysis. Applications.
11:00 - 13:00 
International economic systems as complex networks
Networks in economics. Main topological indicators in international exchange networks. Community analysis in economic networks. The World Trade Network.



Participation is open to everybody and free of charge, but the application is mandatory:

  • If you are a PhD student at Politecnico di Milano, you must include the course in your study plan by the usual Webpoliself procedure (read the notes below on the exam for PhD students).
  • In any other case, send an email to Carlo Piccardi ( with your name, department, etc..



If you are a PhD student at Politecnico di Milano and you want to pass the exam of the course (5 credits):

  • You should attend at least 70% of the lectures (that is, at least 4 days out of 6: your signature will be required each half-day).
  • After the end of the course, but before January 1, 2018, write an email to Carlo Piccardi ( Specify whether you are interested in a specific topic and/or in doing the exam under a specific lecturer.
  • You will be assigned to a lecturer, who will entirely take care of your exam. You will agree with him on the topic of your exam: the lecturer will give you a paper (or a small set of papers) to study.
  • You will also agree on the form of your exam: written report (approx. 4-6 pages single space) or oral presentation (approx. 20 minutes, with slides). Both will contain an extended summary of the paper(s) and your personal criticisms on the content and/or style, suggestions for improvements, possible applications, etc. The maximum grade will not be given to reports/presentations missing particularly interesting comments.
  • The exam must be completed (report delivered, or presentation given) by July 1, 2018. Please notice that we cannot accept any unreasonable timing (e.g., due to deadlines in your duties). After the request, it will take about two weeks to assign a paper/lecturer. Then, it is reasonable to expect not less than 30 days to prepare the report/presentation.

The same regulations apply if you are a PhD student of another University and you need to pass an exam (important: you should also sign the attendance sheets).



The course will be held at the Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, via Ponzio 34/5 (building 20), 20133 Milano, in the "Sala Conferenze" (ground floor).

The Department building is located in the Bassini campus of the Politecnico di Milano. It is within walking distance of the stations Piola and Lambrate FS of the Metro (underground) line 2 ("green line"), of the tram lines 23 and 33, of the bus line 93, and of the train station Lambrate FS. For further information on how to reach, you can read these instructions.



For enquiries about the content of the course and for applications, please contact Carlo Piccardi (

PhD students of Politecnico doctoral programs, please contact your PhD secretariat for any enquiry about the application procedure or any other administrative information.