In recent years, algorithms and neural architectures based on the Weisfeiler-Leman
algorithm, a well-known heuristic for the graph isomorphism problem, have emerged as a …

Vector representations of graphs and relational structures, whether hand-crafted feature
vectors or learned representations, enable us to apply standard data analysis and machine …

Graph neural networks (GNNs) are deep learning architectures for machine learning
problems on graphs. It has recently been shown that the expressiveness of GNNs can be …

Graph kernels based on the $1 $-dimensional Weisfeiler-Leman algorithm and
corresponding neural architectures recently emerged as powerful tools for (supervised) …

While message-passing graph neural networks have clear limitations in approximating
permutation-equivariant functions over graphs or general relational data, more expressive …

Numerous recent works have analyzed the expressive power of message-passing graph
neural networks (MPNNs), primarily utilizing combinatorial techniques such as the $1 …

Recently, many works studied the expressive power of graph neural networks (GNNs) by
linking it to the $1 $-dimensional Weisfeiler-Leman algorithm ($1\text {-}\mathsf {WL} $) …

Over 50 years ago, Lovász proved that two graphs are isomorphic if and only if they admit
the same number of homomorphisms from any graph. Other equivalence relations on …

We present a strong connection between quantum information and the theory of quantum
permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs …

Two graphs G and H are homomorphism indistinguishable over a graph class F if for all
graphs F∈ F the number of homomorphisms from F to G is equal to the number of …