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.

scholarly journals Computational Properties of General Indices on Random Networks

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1341 ◽  
Author(s):  
R. Aguilar-Sánchez ◽  
I. F. Herrera-González ◽  
J. A. Méndez-Bermúdez ◽  
José M. Sigarreta
Keyword(s):  
Matrix Theory ◽  
Random Network ◽  
Scaling Law ◽  
Network Models ◽  
Network Size ◽  
Topological Indices ◽  
Random Networks ◽  
Theory Approach ◽  
Complexity Measures ◽  
Computational Properties

We perform a detailed (computational) scaling study of well-known general indices (the first and second variable Zagreb indices, M1α(G) and M2α(G), and the general sum-connectivity index, χα(G)) as well as of general versions of indices of interest: the general inverse sum indeg index ISIα(G) and the general first geometric-arithmetic index GAα(G) (with α∈R). We apply these indices on two models of random networks: Erdös–Rényi (ER) random networks GER(nER,p) and random geometric (RG) graphs GRG(nRG,r). The ER random networks are formed by nER vertices connected independently with probability p∈[0,1]; while the RG graphs consist of nRG vertices uniformly and independently distributed on the unit square, where two vertices are connected by an edge if their Euclidean distance is less or equal than the connection radius r∈[0,2]. Within a statistical random matrix theory approach, we show that the average values of the indices normalized to the network size scale with the average degree k of the corresponding random network models, where kER=(nER−1)p and kRG=(nRG−1)(πr2−8r3/3+r4/2). That is, X(GER)/nER≈X(GRG)/nRG if kER=kRG, with X representing any of the general indices listed above. With this work, we give a step forward in the scaling of topological indices since we have found a scaling law that covers different network models. Moreover, taking into account the symmetries of the topological indices we study here, we propose to establish their statistical analysis as a generic tool for studying average properties of random networks. In addition, we discuss the application of specific topological indices as complexity measures for random networks.

scholarly journals Random-matrix-theory approach to mesoscopic fluctuations of heat current

2013 ◽  
Vol 88 (2) ◽  
Author(s):  
Martin Schmidt ◽  
Tsampikos Kottos ◽  
Boris Shapiro
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Heat Current ◽  
Theory Approach

Collective behavior of stock price movements—a random matrix theory approach

2001 ◽  
Vol 299 (1-2) ◽  
pp. 175-180 ◽  
Author(s):  
V. Plerou ◽  
P. Gopikrishnan ◽  
B. Rosenow ◽  
L.A.N. Amaral ◽  
H.E. Stanley
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Collective Behavior ◽  
Stock Price ◽  
Matrix Theory ◽  
Theory Approach ◽  
Price Movements ◽  
Stock Price Movements
Sign in / Sign up

Export Citation Format

Share Document