# Tackling Information Asymmetry in Networks: A New Entropy-Based Ranking Index

## Abstract

Information is a valuable asset in socio-economic systems, a significant part of which is entailed into the network of connections between agents. The different interlinkages patterns that agents establish may, in fact, lead to asymmetries in the knowledge of the network structure; since this entails a different ability of quantifying relevant, systemic properties (e.g. the risk of contagion in a network of liabilities), agents capable of providing a better estimation of (otherwise) inaccessible network properties, ultimately have a competitive advantage. In this paper, we address the issue of quantifying the information asymmetry of nodes: to this aim, we define a novel index—InfoRank—intended to rank nodes according to their information content. In order to do so, each node ego-network is enforced as a constraint of an entropy-maximization problem and the subsequent uncertainty reduction is used to quantify the node-specific accessible information. We, then, test the performance of our ranking procedure in terms of reconstruction accuracy and show that it outperforms other centrality measures in identifying the “most informative” nodes. Finally, we discuss the socio-economic implications of network information asymmetry.

## Keywords

Complex networks Shannon entropy Information theory Ranking algorithm## Notes

### Acknowledgements

PB and TS acknowledge support from: FET Project DOLFINS No. 640772 and FET IP Project MULTIPLEX No. 317532.

## References

- 1.Newman, M.E.J.: Networks: An Introduction. Oxford University Press, New York (2010)CrossRefzbMATHGoogle Scholar
- 2.Bloch, F., Jackson, M.O., Tebaldi, P.: Centrality measures in networks (2017). arXiv:1608.05845
- 3.Borgatti, S.P.: Centrality and network flow. Soc. Netw.
**27**, 55–71 (2005)CrossRefGoogle Scholar - 4.Benzi, M., Klymko, C.: A matrix analysis of different centrality measures. SIAM J. Matrix Anal. Appl.
**36**, 686–706 (2013). https://doi.org/10.1137/130950550 CrossRefzbMATHGoogle Scholar - 5.Sabidussi, G.: The centrality index of a graph. Psychometrika
**31**, 581–603 (1966)MathSciNetCrossRefzbMATHGoogle Scholar - 6.Langville, A.N., Meyer, C.: Google’s PageRank and Beyond. Princeton University Press, Princeton (2006)zbMATHGoogle Scholar
- 7.Squartini, T., Cimini, G., Gabrielli, A., Garlaschelli, D.: Network reconstruction via density sampling. Appl. Netw. Sci.
**2**(3) (2017). https://doi.org/10.1007/s41109-017-0021-8 - 8.Zhang, Q., Meizhu, L., Yuxian, D., Yong, D.: Local structure entropy of complex networks (2014). arXiv:1412.3910v1
- 9.Bianconi, G., Pin, P., Marsili, M.: Assessing the relevance of node features for network structure. PNAS
**106**(28), 11433–11438 (2009). https://doi.org/10.1073/pnas.0811511106 ADSCrossRefGoogle Scholar - 10.Bianconi, G.: The entropy of randomized network ensembles. Europhys. Lett.
**81**(2), 28005 (2007)ADSMathSciNetCrossRefGoogle Scholar - 11.Borgatti, S.P.: Identifying sets of key players in a social network. Comput. Math. Organ. Theory
**12**, 21–34 (2006). https://doi.org/10.1007/s10588-006-7084-x CrossRefzbMATHGoogle Scholar - 12.Park, J., Newman, M.E.J.: The statistical mechanics of networks. Phys. Rev. E
**70**, 066117 (2004). https://doi.org/10.1103/PhysRevE.70.066117 ADSMathSciNetCrossRefGoogle Scholar - 13.Squartini, T., Garlaschelli, D.: Maximum-Entropy Networks. Pattern Detection, Network Reconstruction and Graph Combinatorics. Springer Briefs in Complexity. Springer, Cham (2018)zbMATHGoogle Scholar
- 14.Oshio, K., Iwasaki, Y., Morita, S., Osana, Y., Gomi, S., Akiyama, E., Omata, K., Oka, K., Kawamura, K.: Tech. Rep. of CCeP, Keio Future 3. Keio University, Tokyo (2003)Google Scholar
- 15.Colizza, V., Pastor-Satorras, R., Vespignani, A.: Reaction-diffusion processes and metapopulation models in heterogeneous networks. Nat. Phys.
**3**, 276–282 (2007)CrossRefGoogle Scholar - 16.Martinez, N.D.: Artifacts or attributes? Effects of resolution on the Little Rock Lake food web. Ecol. Monogr.
**61**(4), 367–392 (1991)CrossRefGoogle Scholar - 17.Fortunato, S., Boguna, M., Flammini, A., Menczer, F.: Approximating PageRank from in-Degree in Lecture Notes in Computer Science 4936. Springer, Berlin (2008)zbMATHGoogle Scholar
- 18.Gleditsch, K.S.: Expanded trade and GDP data. J. Confl. Resolut.
**46**, 712–724 (2002)CrossRefGoogle Scholar - 19.Squartini, T., Fagiolo, G., Garlaschelli, D.: Randomizing world trade. I. A binary network analysis. Phys. Rev.
**E84**, 046117 (2011). https://doi.org/10.1103/PhysRevE.84.046117 - 20.Wittenberg-Moerman, R.: The role of information asymmetry and financial reporting quality in debt trading: evidence from the secondary loan market. J. Account. Econ.
**46**(2), 240–260 (2008)CrossRefGoogle Scholar - 21.Eisenberg, L., Noe, T.H.: Systemic risk in financial systems. Manag. Sci.
**47**(2), 236–249 (2001)CrossRefzbMATHGoogle Scholar - 22.Rogers, L.C.G., Veraart, L.A.M.: Failure and rescue in an interbank network. Manag. Sci.
**59**(4), 882–898 (2013)CrossRefGoogle Scholar - 23.Barucca, P., Lillo, F.: The organization of the interbank network and how ECB unconventional measures affected the e-MID overnight market (2015). arXiv:1511.08068
- 24.Glasserman, P., Young, P.H.: Contagion in financial networks. J. Econ. Lit.
**54**(3), 779–831 (2016)CrossRefGoogle Scholar - 25.Barucca, P., Bardoscia, M., Caccioli, F., D’Errico, M., Visentin, G., Battiston, S., Caldarelli, G.: Network valuation in financial systems (2016). arXiv:1606.05164