Visualization Tasks for Unlabelled Graphs

TL;DR

The paper addresses a gap in graph visualization by focusing on unlabelled graphs, where node semantics are absent and tasks must rely on topology alone. It introduces a four-layer data abstraction (Augmented, Attributed, Labelled, Unlabelled) to separate unlabelled contexts from richer semantic graphs, and couples this with a Scope+Action+Target taxonomy to systematically enumerate feasible tasks. The authors demonstrate the taxonomy's descriptive, generative, and evaluative power through mapping existing tasks, generating new ones, and conducting a preliminary comparison of six encodings across 17 tasks, using 81 networks as a benchmark. These contributions establish a principled framework for designing, evaluating, and extending invariant-plot visualizations for unlabelled graphs and set the stage for formal human-subject studies and broader ecological validation.

Abstract

We investigate tasks that can be accomplished with unlabelled graphs, which are graphs with nodes that do not have attached persistent or semantically meaningful labels. New visualization techniques to represent unlabelled graphs have been proposed, but more understanding of unlabelled graph tasks is required before these techniques can be adequately evaluated. Some tasks apply to both labelled and unlabelled graphs, but many do not translate between these contexts. We propose a data abstraction model that distinguishes the Unlabelled context from the increasingly semantically rich Labelled, Attributed, and Augmented contexts. We filter tasks collected and gleaned from the literature according to our data abstraction and analyze the surfaced tasks, leading to a taxonomy of abstract tasks for unlabelled graphs. Our task taxonomy is organized according to the Scope of the data at play, the Action intended by the user, and the Target data under consideration. We show the descriptive power of this task abstraction by connecting to concrete examples from previous frameworks, and connect these abstractions to real-world problems. To showcase the evaluative power of the taxonomy, we perform a preliminary assessment of 6 visualizations for each task. For each combination of task and visual encoding, we consider the effort required from viewers, the likelihood of task success, and how both factors vary between small-scale and large-scale graphs.

Figures (5)

• Figure 1: We report on the 65 papers in our literature review, providing first author name and titles for each. The list is organized according to whether we chose previously articulated tasks, gleaned implicitly mentioned tasks, or excluded all tasks from the paper (Tasks). We document whether the paper features a task taxonomy (Taxonomy), publication (Year), and provide the citation (Ref).
• Figure 2: Data abstraction model with an illustrative example. (A) In our data abstraction model, nested layers progressively decrease in semantic richness, shown here from high on the left to low on the right: Augmented is a stand-in term for named graph models with rich associated semantics, in Attributed non-topological semantic information is allowed to be associated with nodes or edges, in Labelled there are persistent unique identifiers that can convey semantic meaning, and Unlabelled is the innermost layer where all semantic information is stripped away, leaving only unique (non-isomorphic) unlabelled graphs. (B) As an illustrative explainer, drawn in red are the 6 unlabelled graphs of 4 nodes. If persistent labels (here shown as node colors) exist, as in the Labelled layer, this set of 6 graphs expands to the set of 38 labelled 4-node graphs. Within each of the 6 groupings based on graph topology (red enclosures) the graphs are structurally equivalent or isomorphic, and distinguishable from each other only through the meaning conveyed through the node labels.
• Figure 3: Our task taxonomy has three dimensions: Scope, Action, and Target. The Scope determines the Action possible to deploy, and which targets from Target are available for an Action to be performed on. (A) We can generate unlabelled graph tasks by combining an Action and a Target at a given Scope. We distinguish with purple the broad-scope Multiple and Pair scopes, and in green the narrow-scope Single, Subgraph, and Constituent scopes (the darker the green hue, the narrower the scope). Our Target list is representative, not exhaustive, in the narrower scopes; at the broad scope, graph is the lone target. (B) Combinatorial space of Scope + Action pairs.
• Figure 4: The six visual encodings we consider for our assessment of unlabelled graph tasks. These six views share the same underlying graph topology: 'moreno-health' from the KONECT repository Konect, an empirical social network of 2539 nodes (people) and 10455 edges (friendships).
• Figure 5: We illustrate the descriptive and evaluative power of our taxonomy by selecting 17 unlabelled graph tasks covering all possible Scope + Action combinations with one or two sampled from Target (rows) to consider with respect to 6 network visualizations (columns). At each task and visual encoding intersection, the table shows our assessment of user performance vs. data scale with a quadrant heatmap: top left for task effort on Small graphs, top right for task success on Small graphs, bottom left for task effort on Large graphs, and bottom right for task success on Large graphs. Task effort and success are indicated with a diverging blue-red colormap mapped to 4 ranked assessment levels: Easy, Middling, Difficult, and Impossible (for task effort); and Always, Sometimes, Rarely, and Never (for task success).