3. Visual Analysis of Weighted Directed Graphs 45
3.3. New Approaches to Visual Analysis of Weighted Directed Graphs
3.3.2. Approach to Visual Analysis of Graphs Using Motifs
Our approach to visual analysis of graphs using motifs is threefold (see Figure3.7). These three sub-approaches are integrated into one system and can be used in combination on demand. Each sub-approach corresponds to one analytical task presented in Section3.1.1. As a basis, search and visualization of found motifs on demand is provided (see Subsection3.3.2.1). The search and visualization methods are applied also to visual analysis of graph changes (see Subsection3.3.2.2). Finally, the visual analysis of large graphs is supported by motif-based graph aggregation (see Subsection3.3.2.3). These approaches are detailed upon in the following.
3.3.2.1. Visual Exploration of Graph Motifs
Visual exploration of graph motifs usually uses graph visualization with highlighting of motifs found in the network (see Figure3.8for an illustration). These approaches however rely on a predefined set of motifs and use global motif search. In practice, the choice of interesting motifs is application, data and task dependent and may even change throughout an analytic process. Against this background, it is difficult to define a complete set of relevant network motifs in advance. Therefore, we also support user-defined motifs in addition to a set of basic graph motifs (see Figure3.20on page71). In order to support an easy input of user motifs, these new motifs can be visually interactively defined by drawing. In addition, we employ local search for motifs (motifs including a specific node or edge), which allow focusing on specific parts of the network and at the same time require less computational time than searching in the whole network. In some cases, specific user-defined constraints on the motifs can be posed, such as minimum edge weight in the motif edges. Therefore we offer also filtering of motifs
3.3. New Approaches to Visual Analysis of Weighted Directed Graphs
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Figure 3.7.: Three types of motif-based visual graph analysis.
according to edge weight criteria. The comparison of our approach with state-of-the-art approaches for visual motif analysis is provided in Figure3.9.
3.3.2.2. Visual Analysis of Graph Changes Using Motifs
Usually, when showing graph dynamics, changes in the graph compared to the previous graph are highlighted (e.g., new/changed edges or nodes). This might be insufficient from an analytical point of view, as for the analyst also the impact of those changes on graph structures can be of high interest. Changes in graph structures can be identified by analyzing the graph for appearance of new or deletion of existing local substructures (motifs). For this purpose, we combine motif analysis with interactive visualization thereby helping to discover indirect effects of graph changes.
The changes can be induced by source data or can be done on demand by the user (in the so-called “what-if-analysis”). In our approach we concentrate on the second case. This type of graph changes is more difficult as it requires also identification of implied graph changes (e.g., node deletion implies changes to the adjacent edges) and the need for tracking of analytic steps for reproducibility of the results.
In our work, we therefore enhance simple visualization of graph changes with identification of implied graph changes, tracking of analytic steps and visualization of impact of changes on local structures. This approach extends significantly other state-of-the art approaches. The comparison of the two methods is provided in Fig-ure3.10.
3.3.2.3. Approach to Visual Analysis of Graphs using Aggregation Based on Motifs
Graph aggregation is often employed for visualization of large graphs as it provides simplification of the original graph. It thereby improves occlusion problems and offers more clear presentation of the data while keeping the structure of the graph. Suitable graph aggregation can support analysis on higher levels of abstraction. For example, in shareholder networks, groups of companies from each sector can be merged into single nodes thereby not only reducing the number of entities in the graph but also allowing for analysis of inter-sectoral relationships in the economy.
Figure 3.8.: An example of the use of visual exploration of graph motifs. Left: State-of-the-art visualization of the whole graph using a node-link diagram showing an overcrowded display, in which the entity relationships are difficult to explore. Right: The result of the new approach showing selected motifs found and filtered in the original graph. This view reveals possibly interesting substructures of the graph in a more easily interpretable way.
There are various methods for the choice of nodes to aggregate, e.g., according to the node properties (such as node betweenness), attribute properties (such as node attribute values) or a predefined node hierarchy. In addition, also interrelationships between local substructures in the network are important to analyze. Therefore, we present a new approach for the visual analysis of large graphs using hierarchic motif-based graph aggregation (see Figure3.11for an illustration). The main advantage of this method is the subsequent merging of local (functional) graph substructures of the input graph thereby revealing their relationships on multiple levels. Our approach is thereby not restricted to a set of predefined aggregation structures. In addition, we also track graph features (e.g., graph size, graph order, number of motifs) in each aggregation step for providing information on the structural changes in the network implied by the aggregation.
The aggregationcan be successively repeatedon the already aggregated graph. The choices of sequence of graph aggregation parameters (e.g., type of graph motif or node attribute) used for aggregation plays a signifi-cant role in the structure of the output graph. Therefore our approach includes tracking of the sequence of the aggregation steps (including their parameters). This should allow for reproducibility and better understanding of the results.
In this thesis, we employ the following threeways of defining group of nodes for aggregation, while concen-trating on motif-based aggregation:
1. interactively user-defined: offers the possibility to flexibly analyze the underlying network without spe-cific criteria. For example, the analysts may want to group companies according to results from previous analysis or her experience.
2. based on node attribute values: offers the possibility to analyze relationships between groups of nodes with the same properties. For example, the analysis of inter-sectoral or inter-regional relationships can be supported in this way.
3.3. New Approaches to Visual Analysis of Weighted Directed Graphs
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(b) New approach to visual motif analysis including also user-defined and local motif search and visualization.
Figure 3.9.: Approaches to visual graph motif analysis. Top: The state-of-the-art approach, bottom: the new approach. The new approach includes also search for user-defined motifs and local search for motifs.
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(b) New approach to visual graph change analysis including also identification of implied graph changes in case of manual graph change, local search and visualization of changes in the motif graph structure as well as calculation and display of changes of graph features.
Figure 3.10.: Approaches to visual graph change analysis. Top: state-of-the-art approach, bottom: new approach.
The new approach also identifies implied changes on the graph substructures and for manual data changes also the need for graph adjustment. It includes also tracking of changes of graph features owing to the data changes. In this way, the implications of the graph changes on the graph structure can be identified.
3.3. New Approaches to Visual Analysis of Weighted Directed Graphs
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Figure 3.11.: An example of motif-based graph aggregation used for graph simplification and visual analysis of relationships between graph substructures on multiple levels of abstraction.
3. motif-based: is suitable for analysis of relationships between specific graph substructures. For example, it can be interesting to examine whether and what type of relationship there is between companies with many shareholders.
Figure 3.12shows the currently used aggregation process (top) and our approach (bottom). Our approach includes also motif-based aggregation and tracking of aggregation parameters. Moreover, tracking of properties of the aggregated graphs at each abstraction level allows for analysis of structural changes owing to the aggrega-tion. The results of each aggregation step are visualized using enhanced visualization tools based on the approach proposed in section3.3.1allowing for exploration of aggregation results.