Carlo Piccardi
DEIB 
Dipartimento di Elettronica, Informazione e
Bioingegneria
Politecnico
di Milano
Piazza
Leonardo da Vinci 32
20133
Milano, Italy
tel
(++39) 02 2399 3566
fax (++39) 02 2399 3412
email carlo.piccardi@polimi.it
web page http://home.deib.polimi.it/piccardi/

[highlights
on recent research]

F.
Calderoni, D. Brunetto, and C. Piccardi, Communities
in criminal networks: A case study,
Social
Networks, 48, 116125, 2017. [doi]
Criminal
organizations tend to be clustered to
reduce risks of detection and
information leaks. Yet, the literature
exploring the relevance of subgroups for
their internal structure is so far very
limited. The paper applies methods of
community analysis to explore the
structure of a criminal network
representing the individuals'
coparticipation in meetings. It draws
from a case study on a large law
enforcement operation (``Operazione
Infinito'') tackling the 'Ndrangheta, a
mafia organization from Calabria, a
southern Italian region. The results
show that the network is indeed
clustered and that communities are
associated, in a non trivial way, with
the internal organization of the
'Ndrangheta into different ``locali''
(similar to mafia families).
Furthermore, the results of community
analysis can improve the prediction of
the ``locale'' membership of the
criminals (up to two thirds of any
random sample of nodes) and the
leadership roles (above 90% precision in
classifying nodes as either bosses or
nonbosses). The implications of these
findings on the interpretation of the
structure and functioning of the
criminal network are discussed.

G. Berlusconi, F. Calderoni,
N. Parolini, M. Verani, and C. Piccardi, Link
prediction in criminal networks: A tool
for criminal intelligence analysis,
PLoS ONE,
11(4): e0154244, 2016. [doi]
The
problem of link prediction has recently
received increasing attention from
scholars in network science. In social
network analysis, one of its aims is to
recover missing links, namely connections
among actors which are likely to exist but
have not been reported because data are
incomplete or subject to various types of
uncertainty. In the field of criminal
investigations, problems of incomplete
information are encountered almost by
definition, given the obvious
antidetection strategies set up by
criminals and the limited investigative
resources. In this paper, we work on a
specific dataset obtained from a real
investigation, and we propose a strategy
to identify missing links in a criminal
network on the basis of the topological
analysis of the links classified as
marginal, i.e. removed during the
investigation procedure. The main
assumption is that missing links should
have opposite features with respect to
marginal ones. Measures of node similarity
turn out to provide the best
characterization in this sense. The
inspection of the judicial source
documents confirms that the predicted
links, in most instances, do relate actors
with large likelihood of coparticipation
in illicit activities.

I. Cingolani, C. Piccardi,
and L. Tajoli,
Discovering preferential patterns in
sectoral trade networks, PLoS ONE, 10(10),
e0140951,
2015. [doi]
We
analyze the patterns of import/export
bilateral relations, with the aim of
assessing the relevance and shape of
"preferentiality" in countries' trade
decisions. Preferentiality here is defined
as the tendency to concentrate trade on
one or few partners. With this purpose, we
adopt a systemic approach through the use
of the tools of complex network analysis.
In particular, we apply a pattern
detection
approach based on community and
pseudocommunity analysis, in order to
highlight the groups of countries within
which most of members' trade occur. The
method is applied to two intraindustry
trade networks consisting of 221
countries, relative to the lowtech
"Textiles and Textile Articles" and the
hightech "Electronics" sectors for the
year 2006, to look at the structure of
world trade before the start of the
international financial crisis. It turns
out that the two networks display some
similarities and some differences in
preferential trade patterns: they both
include few significant communities that
define narrow sets of countries trading
with each other as preferential
destinations markets or supply sources,
and they are characterized by the presence
of similar hierarchical structures, led by
the largest economies. But there are also
distinctive features due to the
characteristics of the industries
examined, in which the organization of
production and the destination markets are
different. Overall, the extent of
preferentiality and partner selection at
the sector level confirm the relevance of
international trade costs still today,
inducing countries to seek the highest
efficiency in their trade patterns.

C. Piccardi, A. Colombo,
and R. Casagrandi, Connectivity
interplays with age in shaping
contagion over networks with vital
dynamics, Physical Review E, 91(2),
022809, 2015. [doi]
The
effects of network topology on the
emergence and persistence of infectious
diseases have been broadly explored in
recent years. However, the influence of
the vital dynamics of the hosts (i.e.,
birthdeath processes) on the network
structure, and their effects on the
pattern of epidemics, have received less
attention in the scientific community.
Here, we study
SusceptibleInfectedRecovered(Susceptible)
[SIR(S)] contact processes in standard
networks (of ErdosRenyi and
BarabasiAlbert type) that are subject to
host demography. Accounting for the vital
dynamics of hosts is far from trivial, and
it causes the scalefree networks to lose
their characteristic fattailed degree
distribution.We introduce a broad class of
models that integrate the birth and death
of individuals (nodes) with the simplest
mechanisms of infection and recovery, thus
generating agedegree structured networks
of hosts that interact in a complex
manner. In our models, the epidemiological
state of each individualmay depend both on
the number of contacts (which changes
through time because of the birthdeath
process) and on its age, paving the way
for a possible agedependent description
of contagion and recovery processes.We
study how the proportion of infected
individuals scales with the number of
contacts among them. Rather unexpectedly,
we discover that the result of highly
connected individuals at the highest risk
of infection is not as general as commonly
believed. In infections that confer
permanent immunity to individuals of vital
populations (SIR processes), the nodes
that are most likely to be infected are
those with intermediate degrees. Our
agedegree structured models allow such
findings to be deeply analyzed and
interpreted, and they may aid in the
development of effective prevention
policies.

F. Della Rossa, M. Gobbi,
G. Mastinu, C. Piccardi, and G.
Previati, Bifurcation analysis of a
car and driver model, Vehicle
System Dynamics, 52, 142156,
2014. [doi]
The bifurcation analysis
of a simple mathematical model describing
a road vehicle with a driver is presented.
The mechanical model of the car has two
degrees of freedom and the related
equations of motion contain the nonlinear
tyre characteristics. The driver is
described by a wellknown model proposed
in the literature. The road vehicle model
has been validated in a case study.
Bifurcation analysis is adopted as the
proper procedure for analysing both
steadystate cornering and straight ahead
motion at different speeds. The importance
of properly computing steadystate
equilibria is highlighted. The effect of a
skilled driver is to broaden the basin of
attraction of stable equilibria and, in
some cases, to stabilise originally
unstable behaviours.Asubcritical Hopf
bifurcation is normally found which limits
the forward speed of either understeering
or oversteering vehicles. A
threeparameter bifurcation analysis is
performed to understand the influence on
stability of driver gain, of driver
prediction time, of vehicle speed. It
turns out, as expected from practice, that
an oversteering vehicle is more
challenging to be controlled than an
understeering one. The paper proposes an
insight into vehicle–driver interaction.
The stabilising or destabilising effect
of the driver is ultimately explained
referring to the existence of a Hopf
bifurcation.

P. Landi and C. Piccardi, Community
analysis in directed networks: In,
out, and pseudocommunities, Physical Review E, 89(1),
012814, 2014. [doi]
When
analyzing important classes of complex
interconnected systems, link directionality
can hardly be
neglected if a precise and effective picture
of the structure and function of the system
is needed. If community
analysis is performed, the notion of
“community” itself is called into question,
since the property of having a comparatively
looser external connectivity could refer to
the inbound or outbound links only or to
both categories. In this paper, we introduce
the notions of in, out, and
in/outcommunity in order to correctly
classify the directedness of the interaction
of a subnetwork with the rest of the system.
Furthermore, we extend the scope of
community analysis by introducing the
notions of in, out, and
in/outpseudocommunity. They are
subnetworks having strong internal
connectivity but also important interactions
with the rest of the system, the latter
taking place by means of a minority of its
nodes only. The various types of
(pseudo)communities are qualified and
distinguished by a suitable set of
indicators and, on a given network, they can
be discovered by using a “local” searching
algorithm. The application to a broad set of
benchmark networks and realworld examples
proves that the proposed approach is able to
effectively disclose the different types of
structures above defined and to usefully
classify the directionality of their
interactions with the rest of the system.
Matlab
code and data used in the paper are
available here.

F. Della Rossa, F. Dercole,
and C. Piccardi, Profiling
coreperiphery network structure by
random walkers, Scientific
Reports, 3, 1467,
2013. [doi]
Disclosing the main
features of the structure of a network is
crucial to understand a number of static
and dynamic properties, such as robustness
to failures, spreading dynamics, or
collective behaviours. Among the possible
characterizations, the coreperiphery
paradigm models the network as the union
of a dense core with a sparsely connected
periphery, highlighting the role of each
node on the basis of its topological
position. Here we show that the
coreperiphery structure can effectively
be profiled by elaborating the behaviour
of a random walker. A curve—the
coreperiphery profile—and a numerical
indicator are derived, providing a global
topological portrait. Simultaneously, a
coreness value is attributed to each node,
qualifying its position and role. The
application to social, technological,
economical, and biological
networks reveals the power of this
technique in disclosing the overall
network structure and the peculiar role
of some specific nodes.
Matlab code and data
used in the paper are available here.

C. Piccardi and L. Tajoli, Existence
and significance of communities in the World
Trade Web, Physical
Review E, 85(6), 066119, 2012. [doi]
TheWorld
TradeWeb (WTW), which models the
international transactions among
countries, is a fundamental tool for
studying the economics of trade flows,
their evolution over time, and their
implications for a number of phenomena,
including the propagation of economic
shocks among countries. In this respect,
the possible existence of communities is a
key point, because it would imply that
countries are organized in groups of
preferential partners. In this paper, we
use four approaches to analyze communities
in the WTW between 1962 and 2008, based,
respectively, on modularity optimization,
cluster analysis, stability functions, and
persistence probabilities. Overall, the
four methods agree in finding no evidence
of significant partitions. A few weak
communities emerge from the analysis, but
they do not represent secluded groups of
countries, as intercommunity linkages are
also strong, supporting the view of a
truly globalized trading system.

C.
Piccardi, Finding and testing
network communities by lumped Markov
chains, PLoS ONE, 6(11),
e27028, 2011. [doi]
Identifying
communities (or clusters), namely groups of
nodes with comparatively strong internal
connectivity, is a
fundamental
task for deeply understanding the structure
and function of a network. Yet, there is a
lack of formal criteria for defining
communities and for testing their
significance. We propose a sharp definition
that is based on a quality threshold. By
means of a lumped Markov chain model of a
random walker, a quality measure called
‘‘persistence probability’’ is associated to
a cluster, which is then defined as an
‘‘alphacommunity’’ if such a probability is
not smaller than a. Consistently, a
partition composed of acommunities is an
‘‘alphapartition.’’ These definitions turn
out to be very effective for finding and
testing communities. If a set of candidate
partitions is available, setting the desired
alevel allows one to immediately select
the
apartition with the finest decomposition.
Simultaneously, the persistence
probabilities quantify the quality of each
single community. Given its ability in
individually assessing each single cluster,
this approach can also disclose single well
defined communities even in networks that
overall do not possess a definite
clusterized structure.
Matlab code and
data used in the paper are available here. 

