# Toward Measuring Network Aesthetics Based on Symmetry

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## Abstract

**:**

## 1. Introduction

- order O (e.g., symmetry of a polygon),
- complexity C (e.g., number of straight lines of a polygon),

## 2. Quantitative Methods and Network Aesthetic Measurement

`R`-based network visualization tool NetBioV [48]. By contrast, the network in Figure 2b represents a transcriptional regulatory network inferred from yeast (see also [49]). These two networks are both undirected and unlabeled, and it should be noted that our definition of aesthetics focuses exclusively on structural properties, e.g., symmetry. This concept could easily be extended to include semantic and functional issues. Such an extension would generate a mapping $\mathrm{Style}\left(G\right)=\mathrm{Style}\left(G\right)(\mathrm{struct},\mathrm{sem},\mathrm{funct})$ for measuring aesthetics of structured objects based on the three parameters: structure, semantics, and function. The space of network styles (Style(G)) represents a graph class. So, the mapping enables us to find parameters (e.g., measures) for their structure, semantics, and function in a more simplified space. For example, structural properties can be mapped to the reals. We plan to define this formally and study the properties of such mappings in future work.

## 3. Methods and Discussion

#### 3.1. Graph-Theoretical Definitions

#### 3.2. Results

**Theorem**

**1.**

**Proof.**

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Chen, Z.; Dehmer, M.; Emmert-Streib, F.; Mowshowitz, A.; Shi, Y. Toward Measuring Network Aesthetics Based on Symmetry. *Axioms* **2017**, *6*, 12.
https://doi.org/10.3390/axioms6020012

**AMA Style**

Chen Z, Dehmer M, Emmert-Streib F, Mowshowitz A, Shi Y. Toward Measuring Network Aesthetics Based on Symmetry. *Axioms*. 2017; 6(2):12.
https://doi.org/10.3390/axioms6020012

**Chicago/Turabian Style**

Chen, Zengqiang, Matthias Dehmer, Frank Emmert-Streib, Abbe Mowshowitz, and Yongtang Shi. 2017. "Toward Measuring Network Aesthetics Based on Symmetry" *Axioms* 6, no. 2: 12.
https://doi.org/10.3390/axioms6020012