Eurographics Conference on Visualization (EuroVis) 2013 Volume 32 (2013), Number 3 B. Preim, P. Rheingans, and H. Theisel (Guest Editors) Visual Analysis of Set Relations in a Graph P. Xu1, F. Du2, N. Cao3, C. Shi1, H. Zhou4and H. Qu1 1Hong Kong University of Science and Technology, Hong Kong, China 2Zhejiang University, China 3 IBM T. J. Watson Research Center, USA 4Shenzhen University, China Abstract Many applications can be modeled as a graph with additional attributes attached to the nodes. For example, a graph can be used to model the relationship of people in a social media website or a bibliographical dataset. Meanwhile, additional information is often available, such as the topics people are interested in and the music they listen to. Based on this additional information, different set relationships may exist among people. Revealing the set relationships in a network can help people gain social insight and better understand their roles within a community. In this paper, we present a visualization system for exploring set relations in a graph. Our system is de- signed to reveal three different relationships simultaneously: the social relationship of people, the set relationship among people’s items of interest, and the similarity relationship of the items. We propose two novel visualization designs: a) a glyph-based visualization to reveal people’s set relationships in the context of their social networks; b) an integration of visual links and a contour map to show people and their items of interest which are clustered into different groups. The effectiveness of the designs has been demonstrated by the case studies on two repre- sentative datasets including one from a social music service website and another from an academic collaboration network. Categories and Subject Descriptors (according to ACM CCS): H.5.2 [INFORMATION INTERFACES AND PRE- SENTATION]: User Interface— 1. Introduction observe the effect of homophily, i.e., “similarity breeds con- nection” or “birds of a feather flock together” [MSLC01]. Set relations appear in various contexts in data analysis. In Meanwhile, visualizing the set relations over the item clus- this paper, we focus on the visual representation of set rela- ters can reveal the “traces” of individuals or groups of peo- tions in a social network where each person (node) is related ple in the information context where the items (such as top- to a set of items. This study is motivated by the increasing ics or music) are organized according to their semantic re- popularity of social websites such as Twitter and Facebook lations (i.e. similarity). In summary, the set relations can be where people take an interest in different topics and share observed from two complementary perspectives, in the con- their favorite readings or music. Meanwhile, other datasets text of a social network and in the context of item clusters. such as bibliographic database can also be described in the same way as it contains academic collaboration networks Many visualization techniques for set relations have been and researchers have different ranges of research interests. developed. Existing set visualizations can be roughly di- This kind of data poses many interesting problems for vi- vided into two categories depending on the most impor- sualization. In particular, we intend to develop effective vi- tant relation it intends to depict: (1) those that utilize spa- sual means for 1) studying the correlation between set re- tial positioning to encode some primary dimension (such lations and topological distances in the social network; and as geographical location) of the items, where the set re- 2) observing the distribution and overlaps of the sets with re- lations are sketched on top of the visualization with en- spect to the clusters of the items. The methods can be used to closing contours or continuous lines. This includes Bub- ⃝c 2013 The Author(s) Computer Graphics Forum ⃝c 2013 The Eurographics Association and Blackwell Publish- ing Ltd. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. P. Xu H. Du N. Cao C. Shi H. Zhou & H. Qu / ble Sets [CPC09], LineSets [ARRC11] and most recently uses bubble-like shapes to connect items belonging to the Kelp diagrams [DvKSW12]; (2) those that emphasize set same set. The Bubble Sets approach is especially effec- relations such as overlappings and subset/superset relations tive to reveal set relations over items which have fixed lay- while other semantic relations between the items are not outs like maps. Similar to the Bubble Sets, the LineSets taken into account. This category of visualizations includes method [ARRC11] uses smooth lines to connect items in Venn diagram and Euler diagram [SAA09][RD10]. To the the same set where the items also have fixed layouts. Din- best of our knowledge, there have been no previous visual kla et al. [DvKSW12] developed the Kelp diagram, which means for visualizing set relations in the context of a social is a most recent algorithm for set visualization over preallo- network. cated items. The algorithm employs edge routing in order to avoid misleading crossovers or wrong set item inclusions. In this paper, we propose visual designs depicting the set relations in a social network from two perspectives: 1) a Another line of set visualization techniques does not as- node-link view with nodes represented by glyphs showing sume a fixed layout of the items. The items are spatially correlations between the social distances and the set rela- grouped such that the relations between sets are more rec- tions (subset / superset / overlap); and 2) a visual design de- ognizable. Simonetto et al. [SAA09] and Stapleton et al. lineating sets on a substrate visualization (e.g. contour map) [SRHZ11] developed fully automatic methods to generate which shows the clusters of all the items given their simi- Euler-like diagrams for the visualization of overlapping sets. larities, and allows viewers to observe the distribution of the Riche and Dwyer [RD10] hierarchically organized the inter- items in the sets. We apply the above techniques to two real secting sets such that the Euler diagrams can be more easily datasets. These include one from a social music service web- drawn. site and another from an academic collaboration network. Moreover, sets can be interpreted as hyperedges in a hy- In summary, the major contributions of this paper are: pergraph, where the items are the vertices and each hyper- • a glyph design that facilitates the analysis of homophily edge could consist of multiple vertices. Methods for drawing in social networks where each node corresponds to a set hypergraphs have been studied in the graph drawing commu- of items; nity [JP87][Mäk90][BE01]. Researchers have also investi- • a visual design and layout method for set relation visual- gated the existence of various types of support that would ization with respect to clusters of items; be applied in the drawing of hypergraphs. These include • two case studies based on real datasets that demonstrate planar [KKS09], path-based [BCPS12], and cactus support how the use of the above two visualizations can lead to in- [BCPS11]. teresting findings in some application domains including In this paper, we propose a composited visual design for online social networks and academic collaboration net- visualizing set relations with respect to the clusters of items works. in the data. We also propose methods to address the trade- The rest of the paper is organized as follows. We first in- off between the geometrical simplicity of the visual links troduce the related work in Section 2. The overview of our denoting each set and the preservation of the item locations system is provided in Section 3, followed by the details of with respect to their corresponding clusters. the visualization design in Section 4 and the implementation in Section 5. We then present the experiment results on two 2.2. Visual Analysis of Social Networks datasets and discuss the limitations of our method in Section Many of the current visual analysis systems focus on de- 6. Finally, in Section 7, we conclude the paper and suggest ∗ some future research directions. picting the topologies of the graph structures [vLKS 11] through node-link diagrams, adjacency matrices, or com- binations of the two. Some integrate statistic information ∗ 2. Related Work to enable more effective visual detection [WFC 06][PS08] ∗ Our work draws on research in several categories. In this sec- [BCD 10][KMSH12]. Many of the statistics are node met- tion, we first review the current existing visualization tech- rics derived from either local topological properties (e.g. niques for set relations. Then we discuss some recent re- node degree, clustering coefficient) or global structures (e.g. search works on the visual analysis of graphs. betweenness centrality). The metrics are directly encoded as visual attributes such as spatial position or color. 2.1. Set Relationship Visualization One of the future directions for graph visualization as ∗ noted in a recent survey [vLKS 11] is the integration of var- The representations of set relationships have been studied ious data types in the visual analysis of graphs. Research from the very early days. Euler diagram and Venn diagram efforts have focused on the visualization of heterogeneous have been used extensively. This problem has also received relations (graph involving multiple types of nodes and rela- attentions from visualization researchers. ∗ tions) [CSL 10][DRRD12], and graphs with node attributes Collins et al. [CPC09] presented Bubble Sets which [SA06][Wat06]. We identify that in real social network data, ⃝c 2013 The Author(s) ⃝c 2013 The Eurographics Association and Blackwell Publishing Ltd. P. Xu H. Du N. Cao C. Shi H. Zhou & H. Qu / each person could be associated with a set of items.