Graph Visualization For Geography - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 87

at the highest level, and then drawing deeper and deeper clusters in the hierarchy.
For instance, applying this strategy to the network of Fig. 6.4 a one would first draw
the compound graph of the highest level (containing the yellow, the green and the
pink metanodes), then draw the compound graph contained in the yellow cluster
(containing node “7” and the brown metanode) and finally draw the content of the
brown cluster (containing nodes “6” and “8”). The main drawback of that method
is that one cannot predict the size of each metanode when drawing a cluster. For
instance, when drawing the yellow cluster, one does not know the size of the brown
metanode. To overcome this problem, the bottom-up strategy first draws the deepest
clusters and then draws clusters at lower and lower levels. In Fig. 6.4 a, the brown
cluster would be drawn before the yellow one, and the size of the brown metanode
can therefore be determined before drawing the yellow cluster.
Some particular tools ( Abello, van Ham, & Krishnan , 2006 ; Archambault,
Munzner, & Auber , 2007 , 2008 ) that focus on the visualization of very large graphs
(even those graphs that are too large to fit in memory) support on-demand drawing to
quickly give the user a first picture of the data. Only the highest level of abstraction
is displayed, and on-demand clusters can be drawn in a top-down manner. However,
because these tools use the top-down strategy, metanodes sizes in the representation
do not necessarily correspond to the number of elements they represent.

6.3.3 Compound Visualization Methods

In this section, we present the two compound visualization methods that we call
classical and multiscale compound visualization methods.
In the classical compound visualization, the metanodes appear opaque. Figure 6.5
shows an example of classical compound visualization corresponding to the highest
level of abstraction of the network of Fig. 6.4 . One of the first interactive classical
compound visualization techniques, developed by Schaffer et al. ( 1996 ), shows the
effectiveness of using graph clustering and compound visualization when exploring
large networks. To enable exploration, the authors introduce a variable zoom method
that consists of using a combination of a metanode expansion (or contraction) and
a geometrical fish-eye. While this interaction ( Schaffer et al. , 1996 ) only allows the
expansion of a single metanode, van Ham and van Wijk ( 2004 ) proposed a method
to define the desired level of abstraction.
In contrast to classical compound visualization, multiscale compound
visualization displays both the original graph and the whole hierarchical partition in
a single view. This is done by filling the “interior” of each metanode (that represents
a cluster) with a drawing of the highest level of abstraction (i.e., the compound
graph of the sub-hierarchy). For instance, in Fig. 6.5 b, the interior of the green
metanode is filled with a drawing of the compound graph corresponding to the top
level of the subtree rooted on the green node, here a graph with three vertices and
edges. And the interior of the yellow metanode is filled with an abstraction of the
subgraph it represents, here a compound graph containing the brown metanode and