Syndesmoscope: The Power of Invariant Plots Linked to Traditional Network Views

Syndesmoscope addresses the limitations of traditional network visualization, where the visual appearance of a graph often depends on arbitrary layout algorithms or node labeling. By juxtaposing traditional force-directed views with three distinct invariant plots—Hop-Census, seriated Adjacency Matrix, and the new kSnakes—the system allows users to observe the same graph topology through multiple, structurally-grounded lenses. The system emphasizes two primary interaction techniques: leapfrogging, which links highlighting across different views, and hopscotching, which allows users to iteratively traverse the graph topology by expanding selections between nodes and their incident edges.

A central contribution of this work is the kSnakes plot, which visualizes the intrinsic dense-sparse gradient of a network. By applying k-core and onion decomposition algorithms, the system organizes nodes into hierarchical shells based on their density. These shells are further partitioned into subshells, which are ordered horizontally to highlight internal connectivity relationships. This layout provides a clear, deterministic visual representation of a graph's core-periphery structure that remains consistent regardless of node labels.

Many network analysis tasks, such as identifying bridge edges or characterizing dense clusters, are difficult to perform using a single visualization idiom. Traditional node-link diagrams often suffer from visual clutter or layout instability, while invariant plots have historically been underexplored. Syndesmoscope bridges this gap by providing a coordinated environment where users can leverage the strengths of both traditional and invariant representations. This multi-view approach enables the discovery of mesoscale phenomena—structures that exist between individual nodes and the entire graph—that are otherwise hidden in standard visualizations.