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
e-mail carlo.piccardi@polimi.it
web page http://home.deib.polimi.it/piccardi/


[highlights on recent research]  


M. Bastos, C. Piccardi, M. Levy, N. McRoberts, and M. Lubell, Core-periphery or decentralized? Topological shifts of specialized information on Twitter, Social Networks, 52, 282-293, 2018. [doi]

In this paper we investigate shifts in Twitter network topology resulting from the type of information being shared. We identified communities matching areas of agricultural expertise and measured the core-periphery centralization of network formations resulting from users sharing generic versus specialized information. We found that centralization increases when specialized information is shared and that the network adopts decentralized formations as conversations become more generic. The results are consistent with classical diffusion models positing that specialized information comes with greater centralization, but they also show that users favor decentralized formations, which can foster community cohesion, when spreading specialized information is secondary.

C. Piccardi, M. Riccaboni, L. Tajoli, and Zhen Zhu, Random walks on the world input–output network, Journal of Complex Networks, in press [doi]

Modern production is increasingly fragmented across countries.To disentangle the world production system at sector level, we use the World Input–Output Database to construct the World Input–Output Network (WION) where the nodes are the individual sectors in different countries and the edges are the transactions between them. In order to explore the features and dynamics of the WION, in this article we detect the communities in the WION and evaluate their significance using a random walk Markov chain approach. Our results contribute to the recent stream of literature analysing the role of global value chains in economic integration across countries, by showing global value chains as endogenously emerging communities in the world production system, and discussing how different perspectives produce different results in terms of the pattern of integration.

F. Calderoni, D. Brunetto, and C. Piccardi, Communities in criminal networks: A case study, Social Networks, 48, 116-125, 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' co-participation 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 non-bosses). 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 anti-detection 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 co-participation 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 intra-industry trade networks consisting of 221 countries, relative to the low-tech "Textiles and Textile Articles" and the high-tech "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., birth-death processes) on the network structure, and their effects on the pattern of epidemics, have received less attention in the scientific community. Here, we study Susceptible-Infected-Recovered(-Susceptible) [SIR(S)] contact processes in standard networks (of Erdos-Renyi and Barabasi-Albert type) that are subject to host demography. Accounting for the vital dynamics of hosts is far from trivial, and it causes the scale-free networks to lose their characteristic fat-tailed 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 age-degree 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 birth-death process) and on its age, paving the way for a possible age-dependent 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 age-degree 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, 142-156, 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 well-known 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 steady-state cornering and straight ahead motion at different speeds. The importance of properly computing steady-state 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 three-parameter 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 de-stabilising 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 pseudo-communities, 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-/out-community 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-/out-pseudocommunity. 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 real-world 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 core-periphery 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 core-periphery 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 core-periphery structure can effectively be profiled by elaborating the behaviour of a random walker. A curve—the core-periphery 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 ‘‘alpha-community’’ if such a probability is not smaller than a. Consistently, a partition composed of a-communities is an ‘‘alpha-partition.’’ These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired a-level allows one to immediately select
the a-partition 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.