4 research outputs found
Growing Graphs with Hyperedge Replacement Graph Grammars
Discovering the underlying structures present in large real world graphs is a
fundamental scientific problem. In this paper we show that a graph's clique
tree can be used to extract a hyperedge replacement grammar. If we store an
ordering from the extraction process, the extracted graph grammar is guaranteed
to generate an isomorphic copy of the original graph. Or, a stochastic
application of the graph grammar rules can be used to quickly create random
graphs. In experiments on large real world networks, we show that random
graphs, generated from extracted graph grammars, exhibit a wide range of
properties that are very similar to the original graphs. In addition to graph
properties like degree or eigenvector centrality, what a graph "looks like"
ultimately depends on small details in local graph substructures that are
difficult to define at a global level. We show that our generative graph model
is able to preserve these local substructures when generating new graphs and
performs well on new and difficult tests of model robustness.Comment: 18 pages, 19 figures, accepted to CIKM 2016 in Indianapolis, I
The Infinity Mirror Test for Graph Models
Graph models, like other machine learning models, have implicit and explicit
biases built-in, which often impact performance in nontrivial ways. The model's
faithfulness is often measured by comparing the newly generated graph against
the source graph using any number or combination of graph properties.
Differences in the size or topology of the generated graph therefore indicate a
loss in the model. Yet, in many systems, errors encoded in loss functions are
subtle and not well understood. In the present work, we introduce the Infinity
Mirror test for analyzing the robustness of graph models. This straightforward
stress test works by repeatedly fitting a model to its own outputs. A
hypothetically perfect graph model would have no deviation from the source
graph; however, the model's implicit biases and assumptions are exaggerated by
the Infinity Mirror test, exposing potential issues that were previously
obscured. Through an analysis of thousands of experiments on synthetic and
real-world graphs, we show that several conventional graph models degenerate in
exciting and informative ways. We believe that the observed degenerative
patterns are clues to the future development of better graph models.Comment: This was submitted to IEEE TKDE 2020, 12 pages and 8 figure