Clustering of random networks under topological constraints

2015 ◽  
Author(s):  
Minas Hovhannisyan ◽  
Svetlana Avetisyan
Keyword(s):  
Random Networks ◽  
Topological Constraints

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 ModularBoost: an efficient network inference algorithm based on module decomposition

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Xinyu Li ◽  
Wei Zhang ◽  
Jianming Zhang ◽  
Guang Li
Keyword(s):  
Network Inference ◽  
Detection Methods ◽  
Inference Problem ◽  
Topological Constraints ◽  
Inference Algorithms ◽  
Module Detection ◽  
Series Expression ◽  
Gene Modules ◽  
Inference Methods ◽  
Complicated Task

Abstract Background Given expression data, gene regulatory network(GRN) inference approaches try to determine regulatory relations. However, current inference methods ignore the inherent topological characters of GRN to some extent, leading to structures that lack clear biological explanation. To increase the biophysical meanings of inferred networks, this study performed data-driven module detection before network inference. Gene modules were identified by decomposition-based methods. Results ICA-decomposition based module detection methods have been used to detect functional modules directly from transcriptomic data. Experiments about time-series expression, curated and scRNA-seq datasets suggested that the advantages of the proposed ModularBoost method over established methods, especially in the efficiency and accuracy. For scRNA-seq datasets, the ModularBoost method outperformed other candidate inference algorithms. Conclusions As a complicated task, GRN inference can be decomposed into several tasks of reduced complexity. Using identified gene modules as topological constraints, the initial inference problem can be accomplished by inferring intra-modular and inter-modular interactions respectively. Experimental outcomes suggest that the proposed ModularBoost method can improve the accuracy and efficiency of inference algorithms by introducing topological constraints.

scholarly journals Topological constraints in the reconnection of vortex braids

2021 ◽  
Vol 33 (5) ◽  
pp. 056101
Author(s):  
S. Candelaresi ◽  
G. Hornig ◽  
B. Podger ◽  
D. I. Pontin
Keyword(s):  
Topological Constraints
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