Prof. Rosario Nunzio Mantegna, Central European University, Budapest, HU and University of Palermo, Palermo, IT

Proximity based networks and statistically validated networks in social and economic systems
The most typical set of complex network comprises networks where links are observed between two nodes when a relationship or an event is occurring between them. In addition to this broad class of networks there is a different class of networks. This other class of networks is obtained by using part of the information which is present in a proximity matrix (either a similarity matrix or a dissimilarity matrix) of the elements of the complex system of interest. In fact, we have shown [1] that part of the information stored in a proximity matrix can be efficiently and informatively summarized in a network. Examples of proximity based networks are minimum spanning trees [1], planar graphs [2], and partial correlation networks [3]. The topology and structure of these proximity based networks are highly informative with respect to the characteristics of the investigated complex systems [4]. Proximity based networks can also be seen as a filtering procedure of the information present in the proximity matrix. Different filtering procedures select different amount of information. In several cases, also the filtering of ordinary networks can be highly informative. The filtering turns out to be very useful when a complex network presents marked deviations form the associated configuration models. We will present and discuss a technique able to statistically validate the over-expression and/or the under-expression of a given pair relationships with respect to the null hypothesis of the configuration model [5]. The technique is quite informative and it is fully taking into account the heterogeneity of the complex system of interest. This technique is used to obtain statistically validated networks [5]. I will discuss applications of these technique on social and economic networks [6] both of ordinary nature as in the case of mobile communication networks [7,8] and proximity based as in the case of surveys [9] or similarity in investment decisions [10].
References:
  1. Mantegna, Rosario N. "Hierarchical structure in financial markets." The European Physical Journal B-Condensed Matter and Complex Systems 11, no. 1 (1999): 193-197.
  2. Tumminello, Michele, Tomaso Aste, Tiziana Di Matteo, and Rosario N. Mantegna. "A tool for filtering information in complex systems." Proceedings of the National Academy of Sciences of the United States of America 102, no. 30 (2005): 10421-10426.
  3. Kenett, Dror Y., Michele Tumminello, Asaf Madi, Gitit Gur-Gershgoren, Rosario N. Mantegna, and Eshel Ben-Jacob. "Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market." PloS one 5, no. 12 (2010): e15032.
  4. Bonanno, Giovanni, Guido Caldarelli, Fabrizio Lillo, and Rosario N. Mantegna. "Topology of correlation-based minimal spanning trees in real and model markets." Physical Review E 68, no. 4 (2003): 046130.
  5. Tumminello, Michele, Salvatore Miccichè, Fabrizio Lillo, Jyrki Piilo, and Rosario N. Mantegna. "Statistically validated networks in bipartite complex systems." PloS one 6, no. 3 (2011): e17994.
  6. Hatzopoulos, Vasilis and Iori, Giulia and Mantegna, Rosario N. and Miccichè, Salvatore and Tumminello, Michele, Quantifying Preferential Trading in the e-MID Interbank Market (October 28, 2013). Quantitative Finance (in press 2015). Available at SSRN: http://ssrn.com/abstract=2343647
  7. Li, Ming-Xia, Zhi-Qiang Jiang, Wen-Jie Xie, Salvatore Miccichè, Michele Tumminello, Wei-Xing Zhou, and Rosario N. Mantegna. "A comparative analysis of the statistical properties of large mobile phone calling networks."Scientific reports 4 (2014).
  8. Ming-Xia Li, Vasyl Palchykov, Zhi-Qiang Jiang, Kimmo Kaski2, János Kertész, Salvatore Miccichè, Michele Tumminello, Wei-Xing Zhou and Rosario N Mantegna, “Statistically validated mobile communication networks: the evolution of motifs in European and Chinese data.” New J. Phys. 16 083038 doi:10.1088/1367-2630/16/8/083038 (2014).
  9. Tumminello, Michele, Salvatore Miccichè, Ligia J. Dominguez, Giovanni Lamura, Maria Gabriella Melchiorre, Mario Barbagallo, and Rosario N. Mantegna. "Happy aged people are all alike, while every unhappy aged person is unhappy in its own way." PloS one 6, no. 9 (2011): e23377.
  10. Tumminello, Michele, Fabrizio Lillo, Jyrki Piilo, and Rosario N. Mantegna. "Identification of clusters of investors from their real trading activity in a financial market." New Journal of Physics 14, no. 1 (2012): 013041.