**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

doi: 10.17586/2226-1494-2016-16-6-1141-1144

doi: 10.17586/2226-1494-2016-16-6-1141-1144

# THE EFFECT OF TOPOLOGY ON TEMPORAL NETWORK DYNAMICS

**Read the full article**';

**Article in**Russian

**For citation:**Guleva V.Y., Amuda A.M., Bochenina K.O., Sloot P.M.A. The effect of topology on temporal network dynamics.

*Scientific and Technical Journal of Information Technologies, Mechanics and Optics*, 2016, vol. 16, no. 6, pp. 1141–1144. doi: 10.17586/2226-1494-2016-16-6-1141-1144

**Abstract**

The effect of initial network topology on a temporal network dynamics is studied. An example of interbank exposures network is considered. It is modeled with a graph, where banks are represented by nodes and interbank lending is represented by edges. The dynamical processes in аtemporal network are defined by state changes of nodes and lie in edges and nodes addition and deletion in a graph, and modification of node states contribute to network evolution. The algorithm of network modification over the whole evolution period is fixed. We present parameters of random, scale free and small world generative models corresponding to different simulation results with fixed modification algorithms. The influence of initial graph topologies on temporal network dynamics is demonstrated. The results obtained give the possibility to assess time interval before the attainment of unstable topology state, and to estimate an optimal topology for the transition to a steady state under fixed modification algorithms.

**Keywords:**complex networks, temporal graph, graph topology, complex systems, banking system, system evolution, modeling

**Acknowledgements.**This paper is financially supported by The Russian Scientific Foundation, Agreement No.14–21–00137 (15.08.2014)

**References**

1. Roukny T., Bersini H., Pirotte H., Caldarelli G., Basttiston S. Default cascades in complex networks: topology and systemic risk // Scientific Reports. 2013. V. 3. Art. 2759.

doi: 10.1038/srep02759

2. May R.M., Arinaminpathy N. Systemic risk: the dynamics of model banking systems // Journal of the Royal Society Interface. 2010. V. 7. N 46. P. 823–838. doi: 10.1098/rsif.2009.0359

3. Purica I. Nonlinear Dynamics of Finantial Crises: How to Predict Discontinuous Decisions. NY: Academic Press, 2015. 124 p.

4. Montagna M., Kok C. Multi-layered interbank model for assessing systemic risk. Kiel Working Paper, 2013. N 1873.

5. Guleva V.Y. The combination of topology and nodes’ states dynamics as an early-warning signal of critical transition in a banking network model // Procedia Computer Science. 2016. V. 80. P. 1755–1764. doi: 10.1016/j.procs.2016.05.436

6. Ye C., Torsello A., Wilson R.C., Hancock E.R. Thermodynamics of time evolving networks // Lecture Notes in Computer Science. 2015. V. 9069. P. 315–324. doi: 10.1007/978-3-319-18224-7_31

7. Mohar B. The Laplacian spectrum of graphs / In: Graph Theory, Combinatorics, and Applications. Wiley, 1991. V. 2. P. 871–898.

8. Chung F.R.K., Lu L. Complex Graphs and Networks. Providence: American Mathematical Society, 2006. V. 107. 264 p.