Learning Hyperedge Replacement Grammars for Graph Generation

Abstract

The discovery and analysis of network patterns is central to the scientific enterprise. In the present work we developed and evaluated a new approach that learns the building blocks of graphs that can be used to understand and generate new realistic graphs. Our key insight is that a graph's clique tree encodes robust and precise information. We show that a Hyperedge Replacement Grammar (HRG) can extracted from the clique tree, and we develop a fixed-size graph generation algorithm that can be used to produce new graphs of a specified size. In experiments on large real-world graphs, we show that graphs generated from the HRG approach exhibit a diverse range of properties that are similar to those found in the original networks. 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 the HRG model can also preserve these local substructures when generating new graphs.

Attributed Graph Modeling with Vertex Replacement Grammars

“…A recent addition to the class of graph generators are hyperedge [9,45] and node replacement [7,8] grammars. Graph grammars contain graphical rewriting rules that match and replace graph fragments, similar to how a context-free string grammar rewrites characters in a string.…”

“…1(A). Attributed Vertex Replacement Grammar (AVRG) builds on recent advances in graph grammars [7][8][9], which were designed 1 The source code is available at https://github.com/satyakisikdar/Attributed-VRG only to model and generate homogeneous graphs, to handle attributed graphs, increasing its applicability to a broad class of modern problems.…”

Learning Context-free Languages with Nondeterministic Stack RNNs

“…Then we use an efficient dynamic programming algorithm to sample strings directly from the distribution of strings in the PCFG with length . This algorithm is adapted from an algorithm presented by Aguinaga et al (2019) for sampling graphs of a specific size from a hyperedge replacement grammar.…”

Towards Interpretable Graph Modeling with Vertex Replacement Grammars

“…Graph Grammar Approaches Other approaches extract a vertex replacement grammar using either a hierarchical clustering [10] or a tree decomposition of a graph [4] to select which nodes to collapse into a grammar rule. These approaches effectively try to form grammar rules from nodes that "go together."…”

“…When the data takes the form of the graph, this goal is expressed as finding meaningful graphical substructures and other patterns that are hidden in the graph. Because of the prevalence of graph data and the importance of this task, dozens of graph models have been developed towards this goal [1]- [4]. Typically, these graph models make some assumptions about the shape or structure of the graph and encode the graph in interesting ways.…”