  Discovering the underlying structures present in large real world graphs is a
fundamental scientific problem. Recent work at the intersection of formal
language theory and graph theory has found that a Hyperedge Replacement Grammar
(HRG) can be extracted from a tree decomposition of any graph. This HRG can be
used to generate new graphs that share properties that are similar to the
original graph. Because the extracted HRG is directly dependent on the shape
and contents of the of tree decomposition, it is unlikely that informative
graph-processes are actually being captured with the extraction algorithm. To
address this problem, the current work presents a new extraction algorithm
called temporal HRG (tHRG) that learns HRG production rules from a temporal
tree decomposition of the graph. We observe problems with the assumptions that
are made in a temporal HRG model. In experiments on large real world networks,
we show and provide reasoning as to why tHRG does not perform as well as HRG
and other graph generators.
