Graphs find its place in many applications like social network analysis, computer vision and bioinformatics. It has the ability to capture the structural relationship among the data, thus provides more insight. Graph Neural Network (GNN) has a deep learning way of analyzing the graph. The target nodes representation is obtained by iterative propagation of neighbour information until the stability is reached. Representational learning is widely used for capturing the insight of graph representation model. The complex structure of graph is hidden by representational learning results in shallow learning mechanism. Convolutional Neural Network (CNN) exploits the stationary properties and hierarchical pattern of the data which are in Euclidean space. Non-Euclidean characteristics of the graph can be captured precisely using graph convolutional neural network. In graph convolution, vertex domain is represented as aggregation of neighbour node’sinformation. In order to encompass the dynamics of graph, diffusion process is used, in which spatial dependency and temporal dependency are considered simultaneously. In Diffusion Convolution Recurrent Neural Network (DCRNN) uses diffusion convolution to capture spatial dependency and Gated Recurrent Unit (GRU) to capture temporal dependency. DCRNN is capable of handling long-term dependencies. In this survey, we conduct comprehensive survey on diffusion convolutional operations on graph, which is one of the most prominent deep learning models for forecasting in time series domain. First, we categorize the variants of graph convolutional models and its convolution operations on graph. Then based on application, graph convolutional models are categorized with their applications. Finally, open challenges in the area of graph convolutional network and future directions for research are discussed.

图在社交网络分析、计算机视觉和生物信息学等许多应用中都占有一席之地。它有能力捕捉数据之间的结构关系，从而提供更多的洞察力。图神经网络 (GNN) 具有分析图的深度学习方式。目标节点表示是通过邻居信息的迭代传播直到达到稳定性得到的。表示学习被广泛用于捕捉图表示模型的洞察力。图的复杂结构被浅层学习机制中的表征学习结果所隐藏。卷积神经网络 (CNN) 利用欧几里得空间中数据的平稳特性和分层模式。使用图卷积神经网络可以精确地捕捉图的非欧几里得特征。在图卷积中，顶点域表示为相邻节点信息的聚合。为了包含图的动态，使用了扩散过程，其中同时考虑了空间依赖性和时间依赖性。在扩散卷积中，循环神经网络 (DCRNN) 使用扩散卷积来捕获空间依赖性，并使用门控循环单元 (GRU) 来捕获时间依赖性。DCRNN 能够处理长期依赖关系。在本次调查中，我们对图上的扩散卷积操作进行了全面调查，图是时间序列域预测中最突出的深度学习模型之一。第一的，我们对图卷积模型的变体及其在图上的卷积操作进行分类。然后根据应用，将图卷积模型与其应用进行分类。最后，讨论了图卷积网络领域的开放挑战和未来的研究方向。