  Recently methods of graph neural networks (GNNs) have been applied to solving
the problems in high energy physics (HEP) and have shown its great potential
for quark-gluon tagging with graph representation of jet events. In this paper,
we introduce an approach of GNNs combined with a HaarPooling operation to
analyze the events, called HaarPooling Message Passing neural network (HMPNet).
In HMPNet, HaarPooling not only extracts the features of graph, but embeds
additional information obtained by clustering of k-means of different particle
features. We construct Haarpooling from five different features: absolute
energy $\log E$, transverse momentum $\log p_T$, relative coordinates
$(\Delta\eta,\Delta\phi)$, the mixed ones $(\log E, \log p_T)$ and $(\log E,
\log p_T, \Delta\eta,\Delta\phi)$. The results show that an appropriate
selection of information for HaarPooling enhances the accuracy of quark-gluon
tagging, as adding extra information of $\log P_T$ to the HMPNet outperforms
all the others, whereas adding relative coordinates information
$(\Delta\eta,\Delta\phi)$ is not very effective. This implies that by adding
effective particle features from HaarPooling can achieve much better results
than solely pure message passing neutral network (MPNN) can do, which
demonstrates significant improvement of feature extraction via the pooling
process. Finally we compare the HMPNet study, ordering by $p_T$, with other
studies and prove that the HMPNet is also a good choice of GNN algorithms for
jet tagging.
