6 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
Towards Interpretable Graph Modeling with Vertex Replacement Grammars
An enormous amount of real-world data exists in the form of graphs.
Oftentimes, interesting patterns that describe the complex dynamics of these
graphs are captured in the form of frequently reoccurring substructures. Recent
work at the intersection of formal language theory and graph theory has
explored the use of graph grammars for graph modeling and pattern mining.
However, existing formulations do not extract meaningful and easily
interpretable patterns from the data. The present work addresses this
limitation by extracting a special type of vertex replacement grammar, which we
call a KT grammar, according to the Minimum Description Length (MDL) heuristic.
In experiments on synthetic and real-world datasets, we show that KT-grammars
can be efficiently extracted from a graph and that these grammars encode
meaningful patterns that represent the dynamics of the real-world system.Comment: 10 pages, 9 figures, accepted at IEEE BigData 201
Modeling Graphs with Vertex Replacement Grammars
One of the principal goals of graph modeling is to capture the building
blocks of network data in order to study various physical and natural
phenomena. Recent work at the intersection of formal language theory and graph
theory has explored the use of graph grammars for graph modeling. However,
existing graph grammar formalisms, like Hyperedge Replacement Grammars, can
only operate on small tree-like graphs. The present work relaxes this
restriction by revising a different graph grammar formalism called Vertex
Replacement Grammars (VRGs). We show that a variant of the VRG called
Clustering-based Node Replacement Grammar (CNRG) can be efficiently extracted
from many hierarchical clusterings of a graph. We show that CNRGs encode a
succinct model of the graph, yet faithfully preserves the structure of the
original graph. In experiments on large real-world datasets, we show that
graphs generated from the CNRG model exhibit a diverse range of properties that
are similar to those found in the original networks.Comment: Accepted as a regular paper at IEEE ICDM 2019. 15 pages, 9 figure