Metabolic networks are almost nonfractal: A comprehensive evaluation

Takemoto, Kazuhiro

doi:10.1103/physreve.90.022802

Cited by 13 publications

(8 citation statements)

References 35 publications

(98 reference statements)

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“…Additionally, the fractal and self-similar properties are widely applied in biological systems, including development of the algorithm to count the motifs in the biological networks [265], prediction of essential genes [305], and measuring the importance of proteins [306]. However, different from the previous view [288] in which metabolic networks exhibit self-similarity (fractality) using a box-counting method, Takemoto [307] found that metabolic networks are almost non-fractal for the increase in network density of the latest metabolic network data, highlighting the needs for a more suitable definition and careful examination of network fractal and self-similarity properties.…”

Section: Fractal and Self-similaritymentioning

confidence: 99%

Computational network biology: Data, models, and applications

et al. 2020

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Biological entities are involved in intricate and complex interactions, in which uncovering the biological information from the network concepts are of great significance. Benefiting from the advances of network science and high-throughput biomedical technologies, studying the biological systems from network biology has attracted much attention in recent years, and networks have long been central to our understanding of biological systems, in the form of linkage maps among genotypes, phenotypes, and the corresponding environmental factors. In this review, we summarize the recent developments of computational network biology, first introducing various types of biological networks and network structural properties. We then review the network-based approaches, ranging from some network metrics to the complicated machine-learning methods, and emphasize how to use these algorithms to gain new biological insights. Furthermore, we highlight the application in neuroscience, human disease, and drug developments from the perspectives of network science, and we discuss some major challenges and future directions. We hope that this review will draw increasing

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Section: Fractal and Self-similaritymentioning

confidence: 99%

Computational network biology: Data, models, and applications

et al. 2020

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“…After computing b( ) for a network, we want to decide whether the network is fractal or not. A typical indicator of a non-fractal network is an exponential form: b( ) ∝ exp(c ), where c is a constant factor [29]. Therefore, comparison of the fitting of the obtained b( ) to power-law and exponential functions enables us to determine the fractality of the network.…”

Section: ) Graph Fractalitymentioning

confidence: 99%

“…Otherwise, it was supposed to be non-fractal. This procedure of fitting and comparison follows that used in [29].…”

Section: A Setupmentioning

confidence: 99%

Fractality of Massive Graphs: Scalable Analysis with Sketch-Based Box-Covering Algorithm

Akiba

Nakamura²,

Takaguchi

2016

2016 IEEE 16th International Conference on Data Mining (ICDM)

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Abstract-Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth processes of networks and to develop useful algorithms. One remarkable example is the fractality of networks, which suggests the self-similar organization of global network structure. To determine the fractality of a network, we need to solve the so-called box-covering problem, where preceding algorithms are not feasible for large-scale networks. The lack of an efficient algorithm prevents us from investigating the fractal nature of large-scale networks. To overcome this issue, we propose a new box-covering algorithm based on recently emerging sketching techniques. We theoretically show that it works in near-linear time with a guarantee of solution accuracy. In experiments, we have confirmed that the algorithm enables us to study the fractality of million-scale networks for the first time. We have observed that its outputs are sufficiently accurate and that its time and space requirements are orders of magnitude smaller than those of previous algorithms.

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“…Regardless of the layout, metabolic networks typically contain many poorly connected nodes interconnected by a few heavily connected nodes (the hubs), the latter being especially associated with cofactors such as ATP, NADH, glutamate and coenzyme A [29] . Consequently, the node connectivity, defined as the number of edges per node, shows a heavy-tailed probability distribution [30] , [31] , [32] , [33] , [34] , [35] , [36] . Furthermore, metabolic networks have a non-random topology and are likely organized in a hierarchical modular structure ( Fig.…”

Section: Introductionmentioning

confidence: 99%