Shareholding Networks and Centrality: An Application to the Italian Financial Market

In this paper we studied the Shareholding Network (SN) embedded in the Italian Stock Market (MIB). We identified the central companies both in the role of transferring information flows and controlling companies. To this end we used betweenness and flow betweenness centrality measures, together with in and out degree. We tested the scale-free property on in and out degree, betweenness and flow betweenness centrality. The effect of external shocks to SN and the different extent on which companies react to them is measured relating asset volatility and betweenness.

[1]  Béla Bollobás,et al.  Random Graphs , 1985 .

[2]  Alessandro Vespignani,et al.  Characterization and modeling of weighted networks , 2005 .

[3]  Michael Mitzenmacher,et al.  A Brief History of Generative Models for Power Law and Lognormal Distributions , 2004, Internet Math..

[4]  Stephen P. Borgatti,et al.  Centrality and network flow , 2005, Soc. Networks.

[5]  P. Bonacich.  Power and Centrality: A Family of Measures , 1987, American Journal of Sociology.

[6]  M. Barthelemy.  Betweenness centrality in large complex networks , 2003, cond-mat/0309436.

[7]  César A. Hidalgo,et al.  Scale-free networks , 2008, Scholarpedia.

[8]  Panos M. Pardalos,et al.  Statistical analysis of financial networks , 2005, Comput. Stat. Data Anal..

[9]  L. Freeman,et al.  Centrality in valued graphs: A measure of betweenness based on network flow , 1991 .

[10]  Frank Harary,et al.  Distance in graphs , 1990 .

[11]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[12]  Phillip Bonacich,et al.  Eigenvector-like measures of centrality for asymmetric relations , 2001, Soc. Networks.

[13]  G. Caldarelli,et al.  Networks of equities in financial markets , 2004 .

[14]  M. Uschold,et al.  Methods and applications , 1953 .

[15]  Rosanna Grassi,et al.  Betweenness Centrality: Extremal Values and Structural Properties , 2009 .

[16]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[17]  John Scott.  What is social network analysis , 2010 .

[18]  A. Nagurney.  Innovations in Financial and Economic Networks , 2003 .

[19]  Guido Caldarelli,et al.  Scale-Free Networks , 2007 .

[20]  S. Borgatti,et al.  Betweenness centrality measures for directed graphs , 1994 .

[21]  Walter Willinger,et al.  Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications , 2005, Internet Math..

[22]  Frank Harary,et al.  Graph Theory , 2016 .

[23]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[24]  Stefano Battiston,et al.  Inner structure of capital control networks , 2004 .

[25]  Alessandro Vespignani,et al.  The effects of spatial constraints on the evolution of weighted complex networks , 2005, physics/0504029.

[26]  Yoshi Fujiwara,et al.  Heterogeneous Economic Networks , 2005, physics/0502005.

[27]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994 .