scholarly journals Invariant Schreier decorations of unimodular random networks

2021 ◽  
Vol 4 ◽  
pp. 1705-1726
Author(s):  
László Márton Tóth
Keyword(s):  
Random Networks

scholarly journals Normalized Sombor Indices as Complexity Measures of Random Networks

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 976
Author(s):  
R. Aguilar-Sánchez ◽  
J. Méndez-Bermúdez ◽  
José Rodríguez ◽  
José Sigarreta
Keyword(s):  
Random Matrix ◽  
Adjacency Matrix ◽  
Matrix Theory ◽  
Computational Study ◽  
Random Networks ◽  
Geometric Graphs ◽  
Theory Approach ◽  
Complexity Measures ◽  
Random Geometric Graphs ◽  
Highly Correlated

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

Asymptotic Secrecy Analysis of Random Networks With Colluding Eavesdroppers

2018 ◽  
Vol 12 (1) ◽  
pp. 871-880 ◽  
Author(s):  
Satyanarayana Vuppala ◽  
Giuseppe Abreu
Keyword(s):  
Random Networks
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