  We introduce Graph Kolmogorov-Arnold Networks (GKAN), an innovative neural
network architecture that extends the principles of the recently proposed
Kolmogorov-Arnold Networks (KAN) to graph-structured data. By adopting the
unique characteristics of KANs, notably the use of learnable univariate
functions instead of fixed linear weights, we develop a powerful model for
graph-based learning tasks. Unlike traditional Graph Convolutional Networks
(GCNs) that rely on a fixed convolutional architecture, GKANs implement
learnable spline-based functions between layers, transforming the way
information is processed across the graph structure. We present two different
ways to incorporate KAN layers into GKAN: architecture 1 -- where the learnable
functions are applied to input features after aggregation and architecture 2 --
where the learnable functions are applied to input features before aggregation.
We evaluate GKAN empirically using a semi-supervised graph learning task on a
real-world dataset (Cora). We find that architecture generally performs better.
We find that GKANs achieve higher accuracy in semi-supervised learning tasks on
graphs compared to the traditional GCN model. For example, when considering 100
features, GCN provides an accuracy of 53.5 while a GKAN with a comparable
number of parameters gives an accuracy of 61.76; with 200 features, GCN
provides an accuracy of 61.24 while a GKAN with a comparable number of
parameters gives an accuracy of 67.66. We also present results on the impact of
various parameters such as the number of hidden nodes, grid-size, and the
polynomial-degree of the spline on the performance of GKAN.
