Computation of document similarity is a critical task in various NLP domains that has applications in deduplication, matching, and recommendation. Traditional approaches for document similarity computation include learning representations of documents and employing a similarity or a distance function over the embeddings. However, pairwise similarities and differences are not efficiently captured by individual representations. Graph representations such as Joint Concept Interaction Graph (JCIG) represent a pair of documents as a joint undirected weighted graph. JCIGs facilitate an interpretable representation of document pairs as a graph. However, JCIGs are undirected, and don't consider the sequential flow of sentences in documents. We propose two approaches to model document similarity by representing document pairs as a directed and sparse JCIG that incorporates sequential information. We propose two algorithms inspired by Supergenome Sorting and Hamiltonian Path that replace the undirected edges with directed edges. Our approach also sparsifies the graph to $O(n)$ edges from JCIG's worst case of $O(n^2)$. We show that our sparse directed graph model architecture consisting of a Siamese encoder and GCN achieves comparable results to the baseline on datasets not containing sequential information and beats the baseline by ten points on an instructional documents dataset containing sequential information.

我们提出了两种方法，将文档对表示为包含顺序信息的有向稀疏JCIG图，其中我们使用Siamese编码器和GCN构建的稀疏有向图模型在不包含顺序信息的数据集上达到与基线模型相当的结果，在包含顺序信息的教学文档数据集上优于基线模型十个百分点。

稀疏图表达工序指导文件