Table-based Visualization and Interaction for Bipartite Graphs
Hans-J¨ org Schulz∗
University of Rostock, Germany
The visualization of bipartite graphs has only recently gained some
interest, as more and more application fields begin to use this spe-
cial graph class as a natural way to encode their data. We present
a table-based approach for the visualization of real world bipartite
graphs, which may be large in size and contain a multitude of at-
tributes. To perform complex selections within such graph data, we
introduce a new script-based brushing mechanism which integrates
naturally with the tabular graph representation.
I.3.8 [Computing Methodologies]: Computer
Graphics—Applications; H.5.2 [Information Systems]: Informa-
tion Interfaces and Presentation—User Interfaces
In graph theory, a graph is called bipartite if its set of vertices
can be partitioned into two disjoint sets, so that within each of
the two sets, there are no adjacent nodes. While bipartite graphs
occur frequently in a variety of application fields  (as movie-
actor-networks, as ontologies, as petri nets, etc.), only recently,
their importance has been noticed and first visualization techniques
appeared: a well adapted node-link-visualization called Anchored
Maps , specific table-based approaches for visual analytics 
and transition graphs [?], as well as some solutions that have been
specifically designed for movie-actor-networks as in the InfoVis
2007 contest . We adapt the idea of a tabular display and ex-
tend it with additional features that allow the technique to scale up
to large networks with a multitude of node attributes. Additionally,
we propose a new script-based method to interactively query and
filter large bipartite graph structures for subgraphs of interest.
Using tables to display the node sets comes as a natural choice,
as every user being familiar with spreadsheet applications is able
to interact with a table instinctively. The two tables representing
the two independent node sets form the basis of our visualization.
So, each row of these tables represents one node and displays the
node attributes. Between these two tables, the connecting edges are
shown as lines, which run from a node’s row within one table to
a row of the other table. Edge weights are mapped onto the width
of the individual edges. Additionally, the two 1-mode projections,
which basically represent paths of length 2, are depicted as arcs at
the side of the two tables. It is apparent that this way of presenting
the graph structure is specifically fitted for bipartite graphs, whose
edges always connect two nodes from the two different node sets,
but never from the same. The overall layout of the described tables,
edges, and arcs is shown in Figure 1.
This basic setup of our table-based visualization technique is
able to represent all features of a bipartite graph, including derived
ones like the projections, in a very compact way. Yet, especially
THE VISUALIZATION TECHNIQUE
large and dense bipartite networks demand some additional features
to minimize visual cluttering and to enhance the accessibility of our
representation. There are basically three problems to target here:
large node sets resulting in long tables, a large edge set causing a
cluttered display between the tables, and large attribute sets leading
to very wide tables. Therefore, the following extensions to the ba-
sic layout address these problems caused by large data sets. They
are marked by their respective letter with which they are shown in
(A) Using a table lens  to reduce the height of the table by
minimizing all rows that are not part of the current region of inter-
est. In our case, the region of interest within a table is defined by
the position of the mouse cursor.
(B) Adding selection markers to the scrollbars to easily find re-
gions with selected rows in large tables and augmenting the scroll-
bars with a fisheye distortion to make clicking an individual marker
and thus jumping to the respective row easier.
(C) Hiding unselected rows to reduce the current view of the ta-
bles to show only selected rows. In this condensed view, unselected
rows will be substituted blockwise by a single row that gives infor-
mation about how many rows have been hidden at that point.
(D) Minimize edge crossings and by this reducing edge clutter.
This is done by reordering tables using a barycentric crossing min-
imization heuristic  as the edges running in between the tables
just follow the ordering of the rows.
(E) Making edges clickable so that a simple mouse click carries
the user right away to an off-screen node without the need to scroll
and visually follow the edges which is possibly obscured by other
(F) Using URL-references to out-source secondary node at-
tributes to HTML pages, from where they can be retrieved on de-
mand. A mouse click on a hyperlinked name or label of a node
opens up an internet browser window that displays the node’s re-
spective HTML page.
However, for further analysis or in-depth visualization of large
bipartite networks, the ability to derive a subset of the entire data
set is also important. This issue is addressed by our structure-based
While gradual selection concepts for data in general  and hierar-
chies in particular  have already been developed, up to this point
no selection method specifically tailored to networks is known. Our
structural selection method fills this gap by adapting the view of
spatial proximity in the graph structure. This means that we are
measuring the distance of a node to a focus node within the graph
structure itself and not within their screen representation. Thus, two
nodes might have been laid out far apart on the screen, but if they
are connected by an edge, their structural proximity is still consid-
ered high. As we want to make the full power of such a structural
selection available to the user, we also strived for increasing its ease
of use. As a result, we decided to split the selection process into an
interactive and an automatic part. For this, the user selects a set of
focus nodes in an interactive first step. This triggers the automated
part, in a second step, which gathers successively all nodes that can
THE STRUCTURE-BASED SELECTION MECHANISM
Figure 1: This screenshot shows the two node sets as tables, the connecting edges in between, and both 1-mode projections at the sides. The
markers point to the special visualization features we added to the basic concept. (A) - Focus+Context in table, (B) - Fisheye scrollbars with
selection markers, (C) - Hide unselected rows, (D) - Minimization of edge crossings, (E) - Clickable edges, (F) - URL-references, (G) - Columns
for the two scripts, (H) - Maximum level of script, (I) - Highlighting of traversed edges and 1-mode projections.
be reached by its predefined, set-based selection logic from the set
of focus nodes.
1st Step: The interactive selection. In our visualization, we
chose a toggling mechanism to mark focus nodes, as it can be seen
in Figure 1. Additionally, the user can just click’n’drag along the
selection columns to select entire regions or intervals of rows. To-
gether with the ability to sort the table with respect to any attribute,
this provides a brushing mechanism that allows to quickly select
items within certain attribute ranges. To enable the comparison of
results from two different selections, two columns are added in both
2nd Step: The automatic selection. The result of the inter-
active selection from the 1st step is passed to the loaded selection
script. Starting with a set that contains only the focus nodes, the
scripted selection logic proceeds to add new node sets script line
by script line in a breadth first manner by traversing along edges or
projections. The paths along which the script traverses the graph
are highlighted in the visual representation of the bipartite graph
(marker (I) in Figure 1) The maximum number of selection levels
can be set interactively from within the visualization, as shown in
Figure 1 at marker (H). Our selection logic allows to define a DoI-
value in every script line, which is then assigned to the node set
added to the selection at this level. In our table-based visualization,
the DoI-values define how the nodes of the set should appear in the
tables: it is used to define the color saturation and the height of the
The presented visualization and selection technique has been suc-
cessfully tested on several real-world data sets from the life sci-
ences, with some of them containing more than 35.000 nodes and
more than 370.000 edges. So far it appears that, because of the pos-
sibility to sort the nodes within the tables by different attributes, the
table-based representation outperforms other display techniques for
bipartite graphs for localization and comparison tasks. Altogether,
the table-based visualization and the script-based selection seem to
provide an efficient way of exploring large bipartite networks.
This work is supported by the DFG graduate school dIEM oSiRiS.
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