Graphlet counting is a widely explored problem in network analysis and has been successfully applied to a variety of applications in many domains, most notatbly bioinformatics, social science, and infrastructure network studies. Efficiently computing graphlet counts remains challenging due to the combinatorial explosion, where a naive enumeration algorithm needs O(Nk) time for k-node graphlets in a network of size N. Recently, many works introduced carefully designed combinatorial and sampling methods with encouraging results. However, the existing methods ignore the fact that graphlet counts and the graph structural information are correlated. They always consider a graph as a new input and repeat the tedious counting procedure on a regular basis even if it is similar or exactly isomorphic to previously studied graphs. This provides an opportunity to speed up the graphlet count estimation procedure by exploiting this correlation via learning methods. In this paper, we raise a novel graphlet count learning (GCL) problem: given a set of historical graphs with known graphlet counts, how to learn to estimate/predict graphlet count for unseen graphs coming from the same (or similar) underlying distribution. We develop a deep learning framework which contains two convolutional neural network models and a series of data preprocessing techniques to solve the GCL problem. Extensive experiments are conducted on three types of synthetic random graphs and three types of real-world graphs for all 3-, 4-, and 5-node graphlets to demonstrate the accuracy, efficiency, and generalizability of our framework. Compared with state-of-the-art exact/sampling methods, our framework shows great potential, which can offer up to two orders of magnitude speedup on synthetic graphs and achieve on par speed on real-world graphs with competitive accuracy.

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学习计数：Graphlet 计数估计的深度学习框架

Graphlet 计数是网络分析中一个被广泛探索的问题，并已成功应用于许多领域的各种应用，尤其是生物信息学、社会科学和基础设施网络研究。由于组合爆炸，有效计算 graphlet 计数仍然具有挑战性，其中一个简单的枚举算法需要 O(ñķ） 的时间ķ- 大小网络中的节点图集ñ. 最近，许多作品介绍了精心设计的组合和采样方法，结果令人鼓舞。然而，现有方法忽略了graphlet计数和图结构信息相关的事实。他们总是将图视为新的输入，并定期重复繁琐的计数过程，即使它与先前研究的图相似或完全同构。这提供了一个机会，通过学习方法利用这种相关性来加速 graphlet 计数估计过程。在本文中，我们提出了一个新的图元计数学习（GCL）问题：给定一组已知图元计数的历史图，如何学习估计/预测来自相同（或相似）底层分布的未见图的图元计数。我们开发了一个深度学习框架，其中包含两个卷积神经网络模型和一系列数据预处理技术解决GCL问题。对所有 3、4 和 5 节点 graphlet 的三种类型的合成随机图和三种类型的真实世界图进行了广泛的实验，以证明我们框架的准确性、效率和通用性。与最先进的精确/采样方法相比，我们的框架显示出巨大的潜力，它可以在合成图上提供高达两个数量级的加速，并在具有竞争准确性的真实世界图上实现同等速度。