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It is challenging for generative models to learn a distribution over graphs because of the lack of permutation invariance: nodes may be ordered arbitrarily across graphs, and standard graph alignment is combinatorial and notoriously…
We introduce a game on graphs. By a theorem of Zermelo, each instance of the game on a finite graph is determined. While the general decision problem on which player has a winning strategy in a given instance of the game is unsolved, we…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional…
We investigate graph representation learning approaches that enable models to generalize across graphs: given a model trained using the representations from one graph, our goal is to apply inference using those same model parameters when…
Depending on the node ordering, an adjacency matrix can highlight distinct characteristics of a graph. Deriving a "proper" node ordering is thus a critical step in visualizing a graph as an adjacency matrix. Users often try multiple matrix…
Graphs constructed to translate some graph problem into another graph problem are usually called auxiliary graphs. Specifically total graphs of simple graphs are used to translate the total colouring problem of the original graph into a…
Recent work at the intersection of formal language theory and graph theory has explored graph grammars for graph modeling. However, existing models and formalisms can only operate on homogeneous (i.e., untyped or unattributed) graphs. We…
A graph is a structure composed of a set of vertices (i.e.nodes, dots) connected to one another by a set of edges (i.e.links, lines). The concept of a graph has been around since the late 19$^\text{th}$ century, however, only in recent…
Graph generation generally aims to create new graphs that closely align with a specific graph distribution. Existing works often implicitly capture this distribution through the optimization of generators, potentially overlooking the…
Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant…
Sentence ordering is to restore the original paragraph from a set of sentences. It involves capturing global dependencies among sentences regardless of their input order. In this paper, we propose a novel and flexible graph-based neural…
We address the problem of predicting the labeling of a graph in an online setting when the labeling is changing over time. We present an algorithm based on a specialist approach; we develop the machinery of cluster specialists which…
We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…
Recently, many graph matching methods that incorporate pairwise constraint and that can be formulated as a quadratic assignment problem (QAP) have been proposed. Although these methods demonstrate promising results for the graph matching…
Graph covers are a way to describe continuous maps (and homeomorphisms) of a Cantor set, more generally than e.g.\ Bratteli-Vershik systems. Every continuous map on a zero-dimensional compact set can be expressed by a graph cover (e.g.\…
Generating graphs from a target distribution is a significant challenge across many domains, including drug discovery and social network analysis. In this work, we introduce a novel graph generation method leveraging $K^2$-tree…
In this paper, author uses set theory to construct a logic model of abstract figure from binary relation. Based on the uniform quantified structure, author gives two logic system for graph traversal and graph coloring respectively, moreover…