scholarly journals Computational analysis of molecular networks using spectral graph theory, complexity measures and information theory

2019 ◽  
Author(s):  
Chien-Hung Huang ◽  
Jeffrey J. P. Tsai ◽  
Nilubon Kurubanjerdjit ◽  
Ka-Lok Ng
Keyword(s):  
Graph Theory ◽  
Frequency Distribution ◽  
Shannon Entropy ◽  
Biological Networks ◽  
Spectral Graph Theory ◽  
Molecular Networks ◽  
Network Motifs ◽  
Complexity Measures ◽  
Spectral Graph ◽  
Graph Energy

AbstractMolecular networks are described in terms of directed multigraphs, so-called network motifs. Spectral graph theory, reciprocal link and complexity measures were utilized to quantify network motifs. It was found that graph energy, reciprocal link and cyclomatic complexity can optimally specify network motifs with some degree of degeneracy. Biological networks are built up from a finite number of motif patterns; hence, a graph energy cutoff exists and the Shannon entropy of the motif frequency distribution is not maximal. Also, frequently found motifs are irreducible graphs. Network similarity was quantified by gauging their motif frequency distribution functions using Jensen-Shannon entropy. This method allows us to determine the distance between two networks regardless of their nodes’ identities and network sizes.This study provides a systematic approach to dissect the complex nature of biological networks. Our novel method different from any other approach. The findings support the view that there are organizational principles underlying molecular networks.

scholarly journals Dissecting molecular network structures using a network subgraph approach

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9556
Author(s):  
Chien-Hung Huang ◽  
Efendi Zaenudin ◽  
Jeffrey J.P. Tsai ◽  
Nilubon Kurubanjerdjit ◽  
Eskezeia Y. Dessie ◽  
...  
Keyword(s):  
Biological Networks ◽  
Spectral Graph Theory ◽  
Molecular Networks ◽  
Driver Genes ◽  
Complexity Measures ◽  
Cellular Processes ◽  
Graph Energy ◽  
Energy Cutoff ◽  
Cancer Networks ◽  
Irreducible Graphs

Biological processes are based on molecular networks, which exhibit biological functions through interactions of genetic elements or proteins. This study presents a graph-based method to characterize molecular networks by decomposing the networks into directed multigraphs: network subgraphs. Spectral graph theory, reciprocity and complexity measures were used to quantify the network subgraphs. Graph energy, reciprocity and cyclomatic complexity can optimally specify network subgraphs with some degree of degeneracy. Seventy-one molecular networks were analyzed from three network types: cancer networks, signal transduction networks, and cellular processes. Molecular networks are built from a finite number of subgraph patterns and subgraphs with large graph energies are not present, which implies a graph energy cutoff. In addition, certain subgraph patterns are absent from the three network types. Thus, the Shannon entropy of the subgraph frequency distribution is not maximal. Furthermore, frequently-observed subgraphs are irreducible graphs. These novel findings warrant further investigation and may lead to important applications. Finally, we observed that cancer-related cellular processes are enriched with subgraph-associated driver genes. Our study provides a systematic approach for dissecting biological networks and supports the conclusion that there are organizational principles underlying molecular networks.

scholarly journals Synchrony and Complexity in State-Related EEG Networks: An Application of Spectral Graph Theory

2020 ◽  
Vol 32 (12) ◽  
pp. 2422-2454
Author(s):  
Amir Hossein Ghaderi ◽  
Bianca R. Baltaretu ◽  
Masood Nemati Andevari ◽  
Vishal Bharmauria ◽  
Fuat Balci
Keyword(s):  
Graph Theory ◽  
Shannon Entropy ◽  
Resting State ◽  
Alpha Rhythm ◽  
Brain Networks ◽  
Spectral Graph Theory ◽  
Random Networks ◽  
Spectral Graph ◽  
The Stability ◽  
The Brain

The brain may be considered as a synchronized dynamic network with several coherent dynamical units. However, concerns remain whether synchronizability is a stable state in the brain networks. If so, which index can best reveal the synchronizability in brain networks? To answer these questions, we tested the application of the spectral graph theory and the Shannon entropy as alternative approaches in neuroimaging. We specifically tested the alpha rhythm in the resting-state eye closed (rsEC) and the resting-state eye open (rsEO) conditions, a well-studied classical example of synchrony in neuroimaging EEG. Since the synchronizability of alpha rhythm is more stable during the rsEC than the rsEO, we hypothesized that our suggested spectral graph theory indices (as reliable measures to interpret the synchronizability of brain signals) should exhibit higher values in the rsEC than the rsEO condition. We performed two separate analyses of two different datasets (as elementary and confirmatory studies). Based on the results of both studies and in agreement with our hypothesis, the spectral graph indices revealed higher stability of synchronizability in the rsEC condition. The k-mean analysis indicated that the spectral graph indices can distinguish the rsEC and rsEO conditions by considering the synchronizability of brain networks. We also computed correlations among the spectral indices, the Shannon entropy, and the topological indices of brain networks, as well as random networks. Correlation analysis indicated that although the spectral and the topological properties of random networks are completely independent, these features are significantly correlated with each other in brain networks. Furthermore, we found that complexity in the investigated brain networks is inversely related to the stability of synchronizability. In conclusion, we revealed that the spectral graph theory approach can be reliably applied to study the stability of synchronizability of state-related brain networks.

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