Large-scale structures in the $\Lambda$CDM Universe: network analysis and machine learning

We perform an analysis of the Cosmic Web as a complex network, which is built on a $\Lambda$CDM cosmological simulation. For each of nodes, which are in this case dark matter halos formed in the simulation, we compute 10 network metrics, which characterize the role and position of a node in the network. The relation of these metrics to topological affiliation of the halo, i.e. to the type of large scale structure, which it belongs to, is then investigated. In particular, the correlation coefficients between network metrics and topology classes are computed. We have applied different machine learning methods to test the predictive power of obtained network metrics and to check if one could use network analysis as a tool for establishing topology of the large scale structure of the Universe. Results of such predictions, combined in the confusion matrix, show that it is not possible to give a good prediction of the topology of Cosmic Web (score is $\approx$ 70 $\%$ in average) based only on coordinates and velocities of nodes (halos), yet network metrics can give a hint about the topological landscape of matter distribution