The readability of networks – how different visual design elements affect the understanding of network data – has been central in network visualization research. However, existing studies have mainly focused on readability induced by topological mapping (based on different layouts) and overlooked the effect of visual aesthetics. Here is proposed a novel experimental framework to study how different network aesthetic choices affect users' abilities of understanding the network structures. The visual aesthetics are grouped in two forms: 1) visual encoding (where the aesthetic mapping depends on the underlying network data) and 2) visual styling (where the aesthetics are applied independent of underlying data). Users are given a simple task – identifying most connected nodes in a network – in a hybrid experimental setting where the visual aesthetic choices are tested in a within-subject manner while the network topologies are tested in a between-subject manner based on a randomized blocking design. This novel experimental design ensures an efficient decoupling of the influence of network topology on readability tests. The utility of different visual aesthetics is measured comprehensively based on task performance (accuracy and time), eye-tracking data, and user feedback (perceived affordance). The results show differential readability effects among choices of visual aesthetics. Particularly, node based visual encoding significantly enhances network readability, specifically glyphs based on their ability to be utilized as a means to allow participants to create more robust strategies in their utilization. The study contributes to both the understanding of the role of visual aesthetics in network visualization design and the experimental design for testing the network readability.