## 1 Introduction
Although this hierarchical structure of the nodes of a graph can be obtained algorithmically, there are multiple domains whose elements intrinsically present a hierarchical structure, such as those based on geographical distributions or biological organisms [3]. In these cases, their study is usually carried out naturally at different scales, with higher levels of aggregation corresponding to higher levels of abstraction. This paper focuses on the design of a visual framework (Carbonic) for the visualization of complex systems that can be represented as a compound graph, i.e., elements hierarchically structured and relations among elements at the finer scale that can be aggregated and studied at other higher scales. This multiscale approach is complemented by additional techniques aimed at reducing visual complexity, not forgetting the prominent role of interaction when visually exploring complex datasets. The interaction capabilities include the possibility of creation and editing so that the designed visual framework allows not only the exploration of existing compound graphs, but also their creation and editing in a visual environment. Multiple areas can benefit from this functionality, such as the addition or creation of synthetic scenes that constitute the input data for subsequent simulation processes or the construction of conceptual maps that allow the understanding of complex issues and their interrelations to understand the landscape of strategic domains either for decision-making or communication purposes. Specifically, Carbonic presents the following main features:  
* Strategies for managing the number of elements to be displayed. Two complementary approaches are provided: the first one discards certain information, either by eliminating particular elements through filter operations or by focusing the display on a subtree through zooming operations. The second approach allows reducing the amount of information by summarizing or aggregating data that are not individually displayed. In this way, groups of nodes can be aggregated into meta-nodes and groups of connections into meta-connections. * Multiscale visualization of the dataset, based on hierarchical aggregations that allow deciding the desired scale for each branch of the tree. Meta-nodes can be selectively collapsed or uncollapsed, depicting the aggregated meta-connections at multi-scale or cross-scale views. Additionally, visual metaphors can be rendered to summarize relevant information from the non-visible collapsed sub-tree. * Techniques for the reduction of visual cluttering, such as edge bundling, transparency, or on-the-fly adjustment of visualization parameters. * Interaction aimed at data exploration for performing topology-based, attribute-based, or browsing tasks. In addition, interaction also provides editing capabilities that allow users to modify an existing dataset or even create a new one from scratch. * Domain awareness taking as input a domain formalization. This guides the definition of filters (adjusting them to the domain properties) and allows defining constraints to guide the modification or creation of the system. The rest of the paper is organized as follows: Section 2 reviews the related work. Section 3 describes the visualization approach followed in Carbonic as well as the strategies applied for complexity management and the provided interaction capabilities. Section 4 presents two use cases applying Carbonic for the interactive exploration and for the visual creation of compound graphs. Finally, we discuss the use cases, provide some conclusions, and point towards future directions.