Department of Biomedical Engineering and Computational Science

Santo Fortunato


Contact information

Email: santo.fortunato (at), santo.fortunato (at)
Mobile: +358 50 460 5511
Room: 3rd floor, F351

Visiting address:
F Building, Rakentajanaukio 2 C, 02150 Espoo

Postal address:
Dept. of Biomedical Engineering and Computational Science,
P.O.Box 12200, FI-00076 Aalto, Finland



  • The special issue Statistical Mechanics and Social Sciences, edited by Michael Macy, Sidney Redner and myself, has just been published in the Journal of Statistical Physics. You can find the contents here (Volume I, Volume II). Read our editorial for a brief overview.
  • My historical-philosophical introduction to the concept of social atom, first class of my course Mathematical modeling of social dynamics, can be seen here
  • My keynote talk Community detection in networks opened the European Conference on Complex Systems 2012 (ECCS'12), Brussels (September the 3rd, 2012)
  • I have been renominated a Distinguished Referee of the journal Europhysics Letters for my referee work in 2011. For more information, please see BECS news.
  • On November the 16th, 2011, I have given my Installation Lecture at Aalto University, a short pedagogical presentation of the history and principles of sociophysics. The video of the lecture can be seen here.
  • I am the winner of the Young Scientist Award for Socio- and Econophysics 2011. The award ceremony was held at the annual meeting of the German Physical Society in Dresden, on March 14th, 2011 (photos: 1, 2, 3, 4). Following the reception of the award, two articles on myself and my work appeared in the newspaper Italia Oggi and in the popular magazine L'Espresso.

Recent papers

  • In the commentary The case for caution in predicting scientists' future impact [Physics Today 66 (4), 8-9, 2013], we warn against the indiscriminate use of quantitative indicators of scientific impact, particularly the h-index, to evaluate academic careers, especially for young scientists.
  • The paper Universality in voting behavior: an empirical analysis (Scientific Reports 3, 1049, 2013) shows that proportional elections with open lists lead to the same pattern for the distribution of performance of candidates across countries and years. Deviations from the general pattern are associated to specific differences in the election rules.
  • In the paper World citation and collaboration networks: uncovering the role of geography in science (Scientific Reports 2, 902, 2012) we study the streams of citations and collaborations between different geographic locations, finding that they obey simple gravity laws.
  • Take a look at our recent paper on the physics of elections: Physics peeks into the ballot box, Physics Today 65 (10), 74-75, 2012.
  • In the paper Characterizing and modeling citation dynamics (PLoS One 6, e24926, 2011) we find that citation distributions of networks of papers of the Americal Physical Society are described by shifted power laws and that citation dynamics is characterized by bursts in the early life of papers. Both features can be accounted for by a modified version of linear preferential attachment, where the paper attractiveness is heterogeneously distributed and decays with time.
  • How do Nobel Prize Laureates accrue their scientific reputation? In the paper How citation boosts promote scientific paradigm shifts and Nobel Prizes (PLoS One 6, e18975, 2011) we show that groundbreaking discoveries make previous publications of the author visible and cited, even in different topics. This "authority effect" is measurable and can be used to distinguish outstanding scholars from normal ones. See the feature by Philip Ball on Nature News!
  • In the paper Finding statistically significant communities in networks (PLoS One 6, e18961, 2011) we present OSLOM, the first multi-purpose method to find communities in graphs, accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics.
  • What are the principles behind the dynamics of online popularity? In the paper Characterizing and modeling the dynamics of online popularity (Phys. Rev. Lett. 105, 158701, 2010) we show that popularity in online media does not change smoothly, but it experiences wild fluctuations, following power law distributions, due to exogenous factors.
  • What do communities in real networks look like? In the paper Characterizing the community structure of complex networks (PLoS One 5, e11976, 2010) we have made a systematic analysis of various networked datasets, finding that communities can be categorized in classes according to their statistical properties and that each class comprises networks of the same (or similar) origin (communication, information, biological, social and technological networks).
  • What is the best algorithm to find communities in networks? In the paper Community detection algorithms: a comparative analysis (Phys. Rev. E 80, 056117, 2009) we have tested the performances of several graph clustering methods on the benchmark graphs we have recently introduced. As a result, the Infomap method by Rosvall and Bergstrom appears to be the most reliable and should be adopted as a first approach, especially when one has no specific information on the network at study.
  • The Website is a portal that computes rankings between physicists, based on the SARA score, a measure of credit defined through the network of citations between scientific authors. The SARA score is described in detail in the paper Diffusion of scientific credits and the ranking of scientists, Physical Review E 80, 056103 (2009). Featured by Physics!
  • In the paper Explosive percolation in scale-free networks (Phys. Rev. Lett. 103, 168701, 2009) we study scale-free networks built with a special process introduced by Achlioptas et al., in which links are placed such to slow down the formation of large clusters. We find that the percolation transition leading to the formation of the giant component displays analytical features at the threshold for any value of the degree exponent λ. For λ>3 the order parameter displays the trivial scaling expected for discontinuous transitions. The percolation threshold is finite for λ>~2.2, in contrast to standard random percolation. In the paper Explosive percolation: A numerical analysis (Phys. Rev. E 81, 036110, 2010) we present a detailed numerical analysis of the process including lattices, random graphs and scale-free networks.
  • The paper Community detection in graphs (Phys. Rep. 486, 75-174, 2010) is the first comprehensive review article on the problem of graph clustering, which consists in identifying clusters of vertices with a high internal density of edges, whereas the density of edges between clusters is comparatively low.

I was born in Augusta (Italy), on May the 31st, 1971. I carried out my undergraduate studies at the Department of Physics and Astronomy of the University of Catania (Italy), where I got my degree on July the 19th, 1995, with the mark of 110/110 cum laude, presenting the thesis "Two-Particle-One-Hole Excitations in the Continuum"

From September 1995 till June 1997 I worked at the Royal Institute of Technology (KTH) of Stockholm, Sweden, supported by a fellowship granted by the Swedish Institute. In Stockholm I kept working on nuclear physics, and specifically on issues related to my thesis work.

In March 1998 I began my PhD studies in the group of Theoretical High Energy Physics at the University of Bielefeld (Germany), which is renowned for its activity in lattice gauge theories. There I developed a theoretical framework that maps the deconfinement transition of SU(2) lattice gauge theory to the percolation transition of special clusters of nearest neighboring like-signed spin variables. I earned my PhD degree on November the 27th, 2000, with the mark of summa cum laude. The title of my PhD thesis was "Percolation and Deconfinement in SU(2) Gauge Theory".

I stayed in Bielefeld as a postdoctoral research associate until December 2004. As a postdoc I basically worked on percolation theory and its possible applications to lattice gauge theories and phenomenology of heavy ion collisions. In summer 2003 I got to know about complex networks at a seminar of my friend and colleague Vito Latora. After some reading, I was fascinated by the new topic, and in general by complex systems, so I decided to join the rapidly increasing scientific community that was dealing with this new research area.

From February 2005 to January 2007 I was postdoctoral research associate at the School of Informatics of Indiana University in Bloomington (Indiana, USA), working in the Complex Systems Group led by Prof. Alessandro Vespignani. During my stay at IU, I worked on several problems, from general theory of complex networks to the study of information and biological networks, to social dynamics.

From February 2007 till September 2009 I was research scientist at the Complex Networks Lagrange Laboratory of the Institute for Scientific Interchange (ISI) in Turin, Italy. Since October 2009 I am research leader at ISI.

In October 2011 I became Associate Professor of Complex Systems of the Department of Biomedical Engineering and Computational Science (BECS) of the School of Science of Aalto University in Espoo, Finland. Since March the 1st, 2014, I am Professor of Complex Systems at BECS.

My research is focused on the area of complex systems. A system is complex when its global properties cannot be simply inferred by extrapolation from the properties of its constituents. The interactions of the constituents are usually simple, but the heterogeneity of the interaction patterns, the presence of nonlinearity and feedback effects give rise to the emergence of global properties/phenomena, involving both the structure and the dynamics of the system. Such emergent properties were not originally designed or imposed to the system from outside, but are a genuine product of self-organization. Examples of complex systems are fractals (see figure), chaotic systems, animal and human societies, the World Wide Web, etc.

The famous Mandelbrot fractal, studied by Benoit Mandelbrot in 1979. Like all fractals, it is a self-similar geometric object, in which each part, however small, looks like the whole.

The field of complex systems is, by its very nature, interdisciplinary. Complex system scientists include physicists, mathematicians, computer scientists, biologists and engineers, with frequent collaborations between scholars with different backgrounds. I am actively working on complex networks theory and applications, and on statistical physics modelling of social dynamics.

Complex networks

A complex network is a graph endowed with the following basic properties:

  • The distribution of the number of adjacent links to a node (degree) is broad, with a tail that often follows a power law
  • The diameter, i.e. the longest of the shortest paths between nodes, is fairly small, growing only logarithmically with the size of the network (small-world phenomenon)
  • The clustering coefficient, i.e. the fraction of closed triads centered at a node, is significantly higher than in a random network with the same number of nodes and links

The field started in 1998 with the seminal paper of Duncan Watts and Steven Strogatz, in which they showed that several networks existing in nature, society and technology, have the small-world property. The interest in this research was boosted by the empirical discoveries of the group of Albert-Lszl Barabsi, revealing that most real networks have a degree distribution with a power law tail. In this way, there is no characteristic value for the degree of a node, that is why people call these graphs scale-free networks.

In the last years, scholars have studied the properties of these networks, proposed models to explain their genesis and evolution, investigated how dynamical processes develop on these special graphs. For an account of the activity in this field we refer to the recent review by Boccaletti et al.

I am especially interested in the problem of the identification of community structure in networks. Real networks display a structure characterized by groups of nodes, called communities or modules, such that nodes of each group share more connections with the other nodes of the group than with the rest of the network. Detecting communities can lead to the discovery of functional units of biological networks, like protein-protein interaction networks or metabolic networks, and disclose unknown properties of nodes. But the problem is hard and still open, in spite of the many approaches which have been suggested over the years. The main difficulty is that it is an ill-defined problem, where there is still confusion about the basic elements, from the definition of community to the evaluation of partitions. Further complications are represented by the fact that nodes can belong to different groups (overlapping communities) and that groups may in turn represent subunits of larger modules (hierarchical structure).

I also study the structure and function of information networks, particularly of the web graph, i.e. the graph where the nodes represent documents of the World Wide Web and the links are the hyperlinks that allow to jump from one web page to another. In particular I investigate the interplay between the web graph structure, search engines and user behavior.

Statistical physics of social dynamics

Society is complex. Social interactions usually involve few individuals, yet non-trivial global phenomena can emerge. For instance, a consensus on some issue can be reached after many discussions between pairs of individuals or within small groups, even if the whole community is large. Similar dynamics can explain how people end up to share a common culture, or language. The global organization of the system can be achieved via simple local interactions between people, just like phase transitions are originated by elementary interactions between neighboring particles/spins. This parallelism is the motivation of the countless applications of statistical physics tools and models to describe large scale social phenomena, like opinion formation, cultural dissemination, language origin and evolution, emergence of hierarchies from initially egalitarian societies, etc.

My main goal is to lay solid foundations to the field, by characterizing large scale social phenomena by means of quantitative regularities. Only in this way it is possible to attempt a quantitative description of social phenomena, which is the best contribution that physicists could give. This can be accomplished by collecting and analyzing data referring to mass phenomena, like elections, marketing, etc. Some recent striking results on elections and voting behavior can be found here. Another possible avenue is to design controlled social experiments by means of the World Wide Web.


Content will be added in the future.

Citation statistics of my papers:

Here are the slides of some talks I have given around the world.

Benchmark graphs to test community detection algorithms

Methods to detect communities in graphs need to be thoroughly tested. To do that, one needs benchmark graphs with a built-in community structure, that the methods should identify. Standard benchmarks, like that by Girvan and Newman, do not account for important features of real networks, like the fat-tailed distributions of node degree and community size. Therefore, we have proposed new classes of benchmark graphs, in which the distributions of node degree and community size are both power laws, with tunable exponents. In the paper Benchmark graphs for testing community detection algorithms, we have proposed a benchmark for the simplest case of undirected and unweighted graphs.

In a more recent paper, entitled Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities, we have extended our benchmark to account for the existence of overlapping communities, and to directed and weighted networks. Recently we have proposed also a hierarchical version of the benchmark, in which clusters are embedded in larger clusters.

  • Package 1 includes the code to generate undirected and unweighted graphs with overlapping communities. The extent of the overlap can be tuned by input, and it can be set to zero if one is interested in non-overlapping clusters.
  • Package 2 includes the code to generate undirected weighted graphs with possibly overlapping communities.
  • Package 3 includes the code to generate directed unweighted graphs with possibly overlapping communities.
  • Package 4 includes the code to generate directed weighted graphs with possibly overlapping communities.
  • Package 5 includes the code to generate the hierarchical benchmarks, with communities inside other communities.

The code is written in C++. In each package there is a Readme file where you can find instructions on how to use the code and simple examples.

Generalized normalized mutual information

In our paper Detecting the overlapping and hierarchical community structure in complex networks (New J. Phys. 11, 033015, 2009) we have introduced a measure of similarity between partitions that can be applied also to compare covers, i.e. divisions of a network into overlapping communities. The measure is based on the normalized mutual information used in information theory and regularly adopted by scholars to compare partitions of a network in communities. The standard normalized mutual information cannot be trivially extended to the case of overlapping communities. The code to compute our new measure for a pair of partitions/covers can be found here. The new measure does not coincide with the standard normalized mutual information when communities do not overlap, but it is quite close. For more information on the measure check this link.