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We proposed the MFMS algorithm [ 8] that first mines maximal frequent edge sets.
Figure 3 shows the percentage of the frequent edge clusters that appear in at least N graphs.
Figure 6 shows the effect of the edge frequency threshold on the percentage of frequent edge clusters.
It is clear that as we increase the edge frequency threshold, the percentage of frequent edge clusters (frequent in at least 7 graphs) increases.
In addition, the runtime for these approaches grows exponentially; even the most efficient ones, such as MULE [ 5] that enumerates maximal frequent edge sets, took almost 57 days for a set of 98 network instances (details available upon request).
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On the other hand, frequent edges in D do not always jointly form frequent subgraph.
Following from Definition 4, we know that it consists of frequent edges.
Such frequent edges form a stable network skeleton shared by majority of the solutions.
Edges that appear in a very small number of graphs will have low co-occurrence similarity with frequent edges and retaining these not-so-frequent edges will lead to a large summary graph and a very sparse edge occurrence matrix.
For example, if we keep the frequent edges that appear in at least 7 graphs, we get a summary graph with with 9,784 nodes and 308,162 edges.
Moreover, edges that appear in a small number of graphs will not be in the edge cluster as their similarities with frequent edges can be below the β threshold.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com