Graph Neural Networks is a neural network architecture that has recently become more common in research publications and real-world applications. And since neural graph networks require modified convolution and pooling operators, many Python packages like PyTorch Geometric, StellarGraph, and DGL have emerged for working with graphs. In Keras Graph Convolutional Neural Network(*kgcnn*) a straightforward and flexible integration of graph operations into the TensorFlow-Keras framework is achieved using *RaggedTensors*. It contains a set of TensorFlow-Keras layer classes that can be used to build graph convolution models. The package also includes standard bench-mark graph datasets such as Cora,45 MUTAG46, and QM9.

The main problem with handling graphs is their variable size. This makes graph data hard to arrange in tensors. For example, placing small charts of different sizes in mini-batches poses a problem with fixed-sized tensors. One way to solve this problem is to use zero-padding with masking or composite tensors. Another is *disjoint representation*. This entails joining the small graphs into a single large graph without connecting the individual subgraphs.

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Graphs are usually represented by an adjacency matrix 𝐴 of shape ([batch], N, N), which has 𝐴_{𝑖𝑗} = 1if the graph has an edge between nodes i and j and 0 otherwise. When represented using Tensors, graphs are stored using:

- Node list
*n*of shape ([batch], N, F) - A connection table of edge indices of incoming and outgoing node
*m*with shape([batch], M, 2) - Corresponding edge feature list e of shape ([batch], M, F).

Here, N denotes the number of nodes, F denotes the node representation dimension, and M the number of edges.

*RaggedTensors* are the TensorFlow equivalent of nested variable-length lists. With *RaggedTensors,* graphs can be represented using just the node features and edge index lists a flexible tensor dimension that incorporates different numbers of nodes and edges. For example, a ragged node tensor of shape ([batch], None, F) can accommodate a flexible graph size in the second dimension.

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A ragged tensor should not be confused with a sparse tensor, it is a dense tensor with an irregular shape. The key difference is that a ragged tensor keeps track of where each row begins and ends, whereas a sparse tensor tracks each item’s coordinates. This difference can be illustrated using the concatenation operation:

**Implementing MEGNet using KCGNN**

- Install KGCNN

Install from source by cloning the repository:

`git clone https://github.com/aimat-lab/gcnn_keras `

`pip install -e ./gcnn_keras `

or install using pip:

`pip install kgcnn`

- Import necessary library and classes

import math import numpy as np import tensorflow as tf import tensorflow.keras as ks import matplotlib.pyplot as plt %matplotlib inline from sklearn.utils import shuffle from kgcnn.data.qm.qm9 import qm9_graph from kgcnn.literature.Megnet import getmodelMegnet,softplus2 from kgcnn.utils.learning import lr_lin_reduction

- Download and prepare the data

# Download Dataset qm9_data = qm9_graph() y_data = qm9_data[0][:,7]*27.2114 #select LUMO in eV x_data = qm9_data[1:] #Scale output y_mean = np.mean(y_data) y_data = (np.expand_dims(y_data,axis=-1)-y_mean) data_unit = 'eV' #Make test/train split VALSIZE = 100 TRAINSIZE = 2000 print("Training Size:",TRAINSIZE," Validation Size:",VALSIZE ) inds = np.arange(len(y_data)) inds = shuffle(inds) ind_val = inds[:VALSIZE ] ind_train = inds[VALSIZE:(VALSIZE + TRAINSIZE)] # Select train/test data xtrain = [[x[i] for i in ind_train] for x in x_data] ytrain = y_data[ind_train] xval = [[x[i] for i in ind_val] for x in x_data] yval = y_data[ind_val]

- Convert the feature lists into RaggedTensors

def make_ragged(inlist): return tf.RaggedTensor.from_row_lengths(np.concatenate(inlist,axis=0), np.array([len(x) for x in inlist],dtype=np.int)) #Make ragged graph tensors plus normal tensor for graph state xval = [make_ragged(x) for x in xval[:3]] + [tf.constant(xval[3])] xtrain = [make_ragged(x) for x in xtrain[:3]] + [tf.constant(xtrain[3])]

- Create and train the model

model = getmodelMegnet( # Input input_node_shape = [None], input_edge_shape = [None,20], input_state_shape = [1], input_node_vocab = 10, input_node_embedd = 16, input_edge_embedd = 16, input_type = 'ragged', # Output output_embedd = 'graph', #Only graph possible for megnet output_use_bias = [True,True,True], output_dim = [32,16,1], output_activation = ['softplus2','softplus2','linear'], output_type = 'padded', #Model specs is_sorted = True, has_unconnected = False, nblocks = 3, n1= 64, n2 = 32, n3= 16, set2set_dim = 16, use_bias = True, act = 'softplus2', l2_coef = None, has_ff = True, dropout = None, dropout_on_predict = False, use_set2set = True, npass= 3, set2set_init = '0', set2set_pool = "sum" ) learning_rate_start = 0.5e-3 learning_rate_stop = 1e-5 epo = 500 epomin = 400 optimizer = tf.keras.optimizers.Adam(lr=learning_rate_start) cbks = tf.keras.callbacks.LearningRateScheduler(lr_lin_reduction(learning_rate_start,learning_rate_stop,epomin,epo)) model.compile(loss='mean_squared_error', optimizer=optimizer, metrics=['mean_absolute_error', 'mean_squared_error']) print(model.summary())

trainlossall = [] testlossall = [] validlossall = [] epostep = 10 hist = model.fit(xtrain, ytrain, epochs=epo, batch_size=64, callbacks=[cbks], validation_freq=epostep, validation_data=(xval,yval), verbose=2 ) trainlossall = hist.history['mean_absolute_error'] testlossall = hist.history['val_mean_absolute_error'] trainlossall =np.array(trainlossall) testlossall = np.array(testlossall) mae_valid = np.mean(np.abs(yval-model.predict(xval)))