A community-imbalanced graph refers to a graph containing multiple communities with large differences in node and edge scales. Graph sampling is a widely used graph reduction technique to accelerate graph computations and simplify graph visualizations. However, existing graph sampling algorithms may encounter several problems, including the loss of small communities, disconnections between communities, and distortions of community scale distribution, on maintaining the community structures in a community-imbalanced graph. In this work, a new quality indicator is proposed to determine if a graph can be regarded as a community-imbalanced graph. A community-imbalanced graph sampling (CIGS) algorithm is proposed to address the community-imbalanced graph sampling problems. Three new evaluation metrics are proposed to assess the performance of community structure maintenance of graph sampling. An algorithm performance experiment and a user study are conducted to evaluate the effectiveness of the proposed CIGS.

Force-directed graph layout methods are widely used in node-link diagram. However, applying uniform force computations to all nodes or node pairs limits their local adjustment ability, which is required to generate specific graph layouts. For example, users may want to increase the repulsive force among a group of densely clustered nodes while keeping the repulsive force among the other nodes unchanged, thereby facilitating the perception of connection structures among the group of nodes. In this study, a unified force-directed graph layout framework supporting local adjustments (GLLA) is proposed. GLLA consists of three core components: two unified parametric force expressions, a unified force model, and an improved stochastic gradient descent-based layout solver. The three components enable GLLA to reproduce the graph layout behaviors of mainstream force-directed algorithms and possess the capability to perform local adjustments on graph layouts. A performance experiment demonstrates that GLLA-implemented graph layouts are comparable to those produced by mainstream force-directed algorithms in graph structure preservation and readability while achieving notable improvements in time performance. Four real-world use cases show that GLLA can satisfy various local adjustment needs in diverse graph layout scenarios.

A time-frequency diagram is a commonly used visualization for observing the time-frequency distribution of radio signals and analyzing their time-varying patterns of communication states in radio monitoring and management. While it excels when performing short-term signal analyses, it becomes inadaptable for long-term signal analyses because it cannot adequately depict signal time-varying patterns in a large time span on a space-limited screen. This research thus presents an abstract signal time-frequency (ASTF) diagram to address this problem. In the diagram design, a visual abstraction method is proposed to visually encode signal communication state changes in time slices. A time segmentation algorithm is proposed to divide a large time span into time slices. Three new quantified metrics and a loss function are defined to ensure the preservation of important time-varying information in the time segmentation. An algorithm performance experiment and a user study are conducted to evaluate the effectiveness of the diagram for long-term signal analyses.