Analysis of Complex
Networks: Theory and Applications
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.
Cadini, Dept. Energy, Politecnico di Milano [webpage]
Renato Casagrandi, DEIB, Politecnico di Milano [webpage] Fabio Dercole, DEIB, Politecnico di
Milano [webpage] Francesca
Mathematics, Politecnico di Milano
Lorenzo Mari, DEIB, Politecnico di
Carlo Piccardi, DEIB, 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 [Piccardi]
and their representation
Examples of real world networks.
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.
Evolutionary games on
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.
Mesoscale network analysis
detection. Modularity. Random-walk-based
9:00 - 10:00 [Ieva]
Latent space models Latent space definition. Inferring the
latent space coordinates. Applications to
10:00 - 13:00 [Cadini]
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
18 9:00 -
13:00 [Casagrandi and Mari]
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
19 9:00 -
Mesoscale network analysis
11:00 - 13:00
systems as complex networks Networks in
topological indicators in international
exchange networks. Community analysis in
economic networks. The World Trade Network.
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).
end of the course, but before January 1, 2018,
write an email to Carlo Piccardi (email@example.com).
Specify whether you are interested in a specific
topic and/or in doing the exam under a specific
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
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
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.