Same Stats, Different Graphs: Exploring the Space of Graphs in Terms of Graph Properties

The Census-Stub Graph Invariant Descriptor

An 'invariant descriptor' captures meaningful structural features of networks, useful where traditional visualizations, like node-link views, face challenges like the 'hairball phenomenon' (inscrutable overlap of points and lines). Designing invariant descriptors involves balancing abstraction and information retention, as richer data summaries demand more storage and computational resources. Building on prior work, chiefly the BMatrix-a matrix descriptor visualized as the invariant 'network portrait' heatmap-we introduce BFS-Census, a new algorithm computing our Census data structures: Census-Node, Census-Edge, and Census-Stub. Our experiments show Census-Stub, which focuses on 'stubs' (half-edges), has orders of magnitude greater discerning power (ability to tell non-isomorphic graphs apart) than any other descriptor in this study, without a difficult trade-off: the substantial increase in resolution doesn't come at a commensurate cost in storage space or computation power. We also present new visualizations-our Hop-Census polylines and Census-Census trajectories-and evaluate them using real-world graphs, including a sensitivity analysis that shows graph topology change maps to visual Census change. Availability: Our Supplemental materials are available at osf.io/nmzra.

Generative network modeling reveals quantitative definitions of bilateral symmetry exhibited by a whole insect brain connectome

Comparing connectomes can help explain how neural connectivity is related to genetics, disease, development, learning, and behavior. However, making statistical inferences about the significance and nature of differences between two networks is an open problem, and such analysis has not been extensively applied to nanoscale connectomes. Here, we investigate this problem via a case study on the bilateral symmetry of a larval Drosophila brain connectome. We translate notions of 'bilateral symmetry' to generative models of the network structure of the left and right hemispheres, allowing us to test and refine our understanding of symmetry. We find significant differences in connection probabilities both across the entire left and right networks and between specific cell types. By rescaling connection probabilities or removing certain edges based on weight, we also present adjusted definitions of bilateral symmetry exhibited by this connectome. This work shows how statistical inferences from networks can inform the study of connectomes, facilitating future comparisons of neural structures.

Visual Comparison of Networks in VR

Networks are an important means for the representation and analysis of data in a variety of research and application areas. While there are many efficient methods to create layouts for networks to support their visual analysis, approaches for the comparison of networks are still underexplored. Especially when it comes to the comparison of weighted networks, which is an important task in several areas, such as biology and biomedicine, there is a lack of efficient visualization approaches. With the availability of affordable high-quality virtual reality (VR) devices, such as head-mounted displays (HMDs), the research field of immersive analytics emerged and showed great potential for using the new technology for visual data exploration. However, the use of immersive technology for the comparison of networks is still underexplored. With this work, we explore how weighted networks can be visually compared in an immersive VR environment and investigate how visual representations can benefit from the extended 3D design space. For this purpose, we develop different encodings for 3D node-link diagrams supporting the visualization of two networks within a single representation and evaluate them in a pilot user study. We incorporate the results into a more extensive user study comparing node-link representations with matrix representations encoding two networks simultaneously. The data and tasks designed for our experiments are similar to those occurring in real-world scenarios. Our evaluation shows significantly better results for the node-link representations, which is contrary to comparable 2D experiments and indicates a high potential for using VR for the visual comparison of networks.