Related papers: A graph isomorphism invariant based on neighborhoo…
Path graphs are intersection graphs of paths in a tree.~In this paper we give a "6\ good characterization" of path graphs, namely, we prove that path graph membership is in $NP\cap CoNP$ without resorting to existing polynomial time…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
In recent years there has been a rapid increase in classification methods on graph structured data. Both in graph kernels and graph neural networks, one of the implicit assumptions of successful state-of-the-art models was that…
We investigate the parameterized complexity of finding subgraphs with hereditary properties on graphs belonging to a hereditary graph class. Given a graph $G$, a non-trivial hereditary property $\Pi$ and an integer parameter $k$, the…
We focus on graph classification using a graph neural network (GNN) model that precomputes the node features using a bank of neighborhood aggregation graph operators arranged in parallel. These GNN models have a natural advantage of reduced…
The computational cost of simulating quantum many-body systems can often be reduced by taking advantage of physical symmetries. While methods exist for specific symmetry classes, a general algorithm to find the full permutation symmetry…
A hallmark of graph neural networks is their ability to distinguish the isomorphism class of their inputs. This study derives hardness results for the classification variant of graph isomorphism in the message-passing model (MPNN). MPNN…
Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering…
A fundamental and challenging problem in spectral graph theory is to characterize which graphs are uniquely determined by their spectra. In Wang [J. Combin. Theory, Ser. B, 122 (2017): 438-451], the author proved that an $n$-vertex graph…
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered…
Graph representation learning (also called graph embeddings) is a popular technique for incorporating network structure into machine learning models. Unsupervised graph embedding methods aim to capture graph structure by learning a…
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…
Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…
Bidimensionality is the most common technique to design subexponential-time parameterized algorithms on special classes of graphs, particularly planar graphs. The core engine behind it is a combinatorial lemma of Robertson, Seymour and…
This paper proposes a family of permutation-invariant graph embeddings, generalizing the Skew Spectrum of graphs of Kondor & Borgwardt (2008). Grounded in group theory and harmonic analysis, our method introduces a new class of graph…
Graph clustering aims at discovering a natural grouping of the nodes such that similar nodes are assigned to a common cluster. Many different algorithms have been proposed in the literature: for simple graphs, for graphs with attributes…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels…
We propose a node clustering method for time-varying graphs based on the assumption that the cluster labels are changed smoothly over time. Clustering is one of the fundamental tasks in many science and engineering fields including signal…
We introduce the class of interval $H$-graphs, which is the generalization of interval graphs, particularly interval bigraphs. For a fixed graph $H$ with vertices $a_1,a_2,\dots,a_k$, we say that an input graph $G$ with given partition…