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. 2017 Jul 14;7(1):5378.
doi: 10.1038/s41598-017-05670-w.

A method for validating Rent's rule for technological and biological networks

Fernando Alcalde Cuesta  1   2 , Pablo González Sequeiros  1   3 , Álvaro Lozano Rojo  4   5   6
Affiliations

A method for validating Rent's rule for technological and biological networks

Fernando Alcalde Cuesta et al. Sci Rep. .

Abstract

Rent's rule is empirical power law introduced in an effort to describe and optimize the wiring complexity of computer logic graphs. It is known that brain and neuronal networks also obey Rent's rule, which is consistent with the idea that wiring costs play a fundamental role in brain evolution and development. Here we propose a method to validate this power law for a certain range of network partitions. This method is based on the bifurcation phenomenon that appears when the network is subjected to random alterations preserving its degree distribution. It has been tested on a set of VLSI circuits and real networks, including biological and technological ones. We also analyzed the effect of different types of random alterations on the Rentian scaling in order to test the influence of the degree distribution. There are network architectures quite sensitive to these randomization procedures with significant increases in the values of the Rent exponents.

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Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Figure 1
Figure 1
The box counting method is applied to procure the Rent characteristic of each network, as well the whole Rent characteristic of a sample of 50 random networks with the same degree distribution. The Rent exponent obtained by a raw regression is compared with the Rent exponent determined after truncate Region II when the coefficient of variation c in the Rentian scaling of the sample is greater than or equal to 0.1. Different results using c ≥ 0.075 have been already reported (see also Table 1).
Figure 2
Figure 2
Recursive bipartitioning is applied to procure the Rent characteristic of each network, as well the whole Rent characteristic of a sample of 50 random network with the same degree distribution. Regressions and Rent exponents of both empirical and random networks are compared.
Figure 3
Figure 3
Recursive bipartitioning is applied to obtain the Rent characteristics of each empirical network and each random network (SA), (CM), (CLM) and (ER) with the same order and size.
Figure 4
Figure 4
The box counting method is applied to obtain the Rent characteristics of each empirical network and each random network (SA), (CM), (CLM) and (ER) with the same order and size.
Figure 5
Figure 5
(a,b) Rent characteristics of the ISPD98 circuit ibm01 with 12,752 nodes and 50,566 edges, which are obtained using the box counting method and recursive bipartitioning. (c,d) Rent characteristics for randomized networks derived from the ISPD98 circuit ibm01.
See this image and copyright information in PMC

References

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