# DepthRank: Exploiting Temporality to Uncover Important Network Nodes

## Abstract

Identifying important network nodes is very crucial for a variety of applications, such as the spread of an idea or an innovation. The majority of the publications so far assume that the interactions between nodes are *static*. However, this approach neglects that real-world phenomena evolve in time. Thus, there is a need for tools and techniques which account for evolution over time. Towards this direction, we present a novel graph-based method, named *DepthRank* (DR) that incorporates the temporal characteristics of the underlying datasets. We compare our approach against two baseline methods and find that it efficiently recovers important nodes on three real world datasets, as indicated by the numerical simulations. Moreover, we perform our analysis on a modified version of the DBLP dataset and verify its correctness using ground truth data.

## Keywords

Influence detection Network analysis Temporal awareness## Notes

### Acknowledgement

This research was performed under the EU’s project “Trusted, Citizen - LEA collaboration over sOcial Networks(TRILLION)” (grant agreement No 653256).

## Supplementary material

## References

- 1.Aggarwal, C.C., Lin, S., Yu, P.S.: On Influential Node Discovery in Dynamic Social Networks, pp. 636–647 (2012)Google Scholar
- 2.Cai, Q., Sun, L., Niu, J., Liu, Y., Zhang, J.: Disseminating real-time messages in opportunistic mobile social networks: a ranking perspective. In: 2015 IEEE International Conference on Communications (ICC), pp. 3228–3233 (2015)Google Scholar
- 3.van Eck, P.S., Jager, W., Leeflang, P.S.H.: Opinion leaders’ role in innovation diffusion: a simulation study. J. Prod. Innov. Manag.
**28**(2), 187–203 (2011)CrossRefGoogle Scholar - 4.Estrada, E.: The Structure of Complex Networks: Theory and Applications. Oxford University Press, Oxford (2011)CrossRefGoogle Scholar
- 5.Gómez-Gardeñes, J., Echenique, P., Moreno, Y.: Immunization of real complex communication networks. Euro. Phys. J. B - Condens. Matter Complex Syst.
**49**(2), 259–264 (2006)CrossRefGoogle Scholar - 6.Jansen, B.J., Zhang, M., Sobel, K., Chowdury, A.: Twitter power: tweets as electronic word of mouth. J. Am. Soc. Inf. Sci. Technol.
**60**(11), 2169–2188 (2009)CrossRefGoogle Scholar - 7.Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2003, New York, NY, USA, pp. 137–146 (2003)Google Scholar
- 8.Kendall, M.G.: A new measure of rank correlation. Biometrika
**30**(1–2), 81 (1938)CrossRefMATHGoogle Scholar - 9.Kitsak, M., Gallos, L., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H., Makse, H.: Identification of influential spreaders in complex networks. Nat. Phys.
**6**(11), 888–893 (2010)CrossRefGoogle Scholar - 10.Laflin, P., Mantzaris, A.V., Ainley, F., Otley, A., Grindrod, P., Higham, D.J.: Discovering and validating influence in a dynamic online social network. Soc. Netw. Anal. Min.
**3**(4), 1311–1323 (2013)CrossRefGoogle Scholar - 11.Lü, L., Chen, D., Ren, X.L., Zhang, Q.M., Zhang, Y.C., Zhou, T.: Vital nodes identification in complex networks. Phys. Rep.
**650**, 1–63 (2016)MathSciNetCrossRefGoogle Scholar - 12.Magnien, C., Tarissan, F.: Time evolution of the importance of nodes in dynamic networks. In: 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), pp. 1200–1207 (2015)Google Scholar
- 13.Michalski, R., Kajdanowicz, T., Bródka, P., Kazienko, P.: Seed selection for spread of influence in social networks: temporal vs. static approach. New Gener. Comput.
**32**(3), 213–235 (2014)CrossRefGoogle Scholar - 14.Morone, F., Makse, H.: Influence maximization in complex networks through optimal percolation. Nature
**524**(7563), 65–68 (2015)CrossRefGoogle Scholar - 15.Newman, M.: Networks: An Introduction. Oxford University Press, New York (2010)CrossRefMATHGoogle Scholar
- 16.Rocha, L., Masuda, N.: Individual-based approach to epidemic processes on arbitrary dynamic contact networks. Scientific Reports 6 (2016)Google Scholar
- 17.Rosas-Casals, M., Valverde, S., Solé, R.V.: Topological vulnerability of the European power grid under errors and attacks. Int. J. Bifurcat. Chaos
**17**(07), 2465–2475 (2007)CrossRefMATHGoogle Scholar - 18.Saramäki, J., Moro, E.: From seconds to months: an overview of multi-scale dynamics of mobile telephone calls. Euro. Phys. J. B
**88**(6), 164 (2015)CrossRefGoogle Scholar - 19.Song, G., Li, Y., Chen, X., He, X., Tang, J.: Influential node tracking on dynamic social network: an interchange greedy approach. IEEE Trans. Knowl. Data Eng.
**29**(2), 359–372 (2017)CrossRefGoogle Scholar - 20.Stehlé, J., Voirin, N., Barrat, A., Cattuto, C., Isella, L., Pinton, J.F., Quaggiotto, M., van den Broeck, W., Régis, C., Lina, B., Vanhems, P.: High-resolution measurements of face-to-face contact patterns in a primary school. PLoS ONE
**6**(8), e23176 (2011)CrossRefGoogle Scholar - 21.Tang, J., Zhang, J., Yao, L., Li, J., Zhang, L., Su, Z.: ArnetMiner: extraction and mining of academic social networks. In: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2008, New York, NY, USA, pp. 990–998 (2008)Google Scholar
- 22.Valdano, E., Ferreri, L., Poletto, C., Colizza, V.: Analytical computation of the epidemic threshold on temporal networks. Phys. Rev. X
**5**, 021005 (2015)Google Scholar - 23.Vestergaard, C., Génois, M.: Temporal gillespie algorithm: fast simulation of contagion processes on time-varying networks. PLoS Comput. Biol.
**11**(10), e1004579 (2015)CrossRefGoogle Scholar - 24.Viswanath, B., Mislove, A., Cha, M., Gummadi, K.P.: On the evolution of user interaction in Facebook. In: Proceedings of the 2nd ACM Workshop on Online Social Networks, WOSN 2009, New York, NY, USA, pp. 37–42 (2009)Google Scholar
- 25.Zhuang, H., Sun, Y., Tang, J., Zhang, J., Sun, X.: Influence maximization in dynamic social networks. In: 2013 IEEE 13th International Conference on Data Mining, pp. 1313–1318 (2013)Google Scholar