Database Reference
In-Depth Information
is focused on a selected node. The neighbourhood setting determines how much
of the surrounding graph is displayed at any one time. This mechanism allows
local regions of a graph to be displayed. Edge manipulation can be done using a
slider that sets the weight threshold below which edges are not displayed. It is
dicult to judge apriori which edges to filter out, as weak edges can obscure the
graph structure in some cases but may be crucial in others. A practical solution
is to create a graph with relatively high connectivity (many weak links), and
then allow the user to remove links in an interactive manner.
The graph layout is done dynamically, and changes smoothly as the user
varies the interactive settings. The graph layout uses various visual properties
of the nodes and edges to convey information, including colour, shape, label,
and mouse-over popup windows. We also allow attributes of the nodes to set the
graph layout. This is particularly useful with spatial and temporal data.
An alternative visualisation option is to save the XML document and import
it into the user's preferred graph software. This might be appropriate with ex-
tremely large graphs, since this visualisation tool does not work well with such
graphs.
2.3
Analytical Tools
The fields of graph theory and data mining have developed a range of algo-
rithms that assess specific properties of graph structures, including subgraph
analyses (e.g. [14, 15, 16, 17, 18]), connectivity and flow [7], graph simplifica-
tion [5, 19], clustering, and outlier detection [20, 21]. Many of the properties
assessed by these tools have interpretations in terms of real-world phenomena
(e.g. [22, 23, 24]) that are not easily assessed from non-graph representations of
the data. These provide useful analytical information to complement existing
scientific analyses, and also the possibility of building graphs based on analyses
of other graphs.
A simple but very useful example is an operator that allows the similarity
between two graphs to be calculated. We use an edge-matching metric, equal to
the number of edges that appear in both graphs, as a fraction of the total number
of unique edges in the two graphs (an edge is considered to appear in both graphs
if the same two nodes appear in both graphs, and they are joined by an edge
in both graphs). This provides a simple method for exploring the relationships
between graphs, and also a mechanism for creating graphs of graphs: given a
set of graphs, one can construct another graph
in which each graph in the set
is represented by a node. Using a graph similarity operator, one can calculate
the similarity between each pair of graphs in the set, and use this similarity
information to create weighted edges between the nodes in
G
. The visualisation
tool allows a node in a graph to be hyperlinked to another graph, so that each
node in a graph of graphs can be explored in its own right. We demonstrate
these ideas in the Results section, below.
We have chosen not to implement other algorithms at this stage, concentrating
instead on the graph construction and visual exploratory aspects. We raise future
algorithm development options in the Discussion section, below.
G
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