Structural roles define sets of structurally similar nodes that are more similar to nodes inside the set than outside, whereas communities define sets of nodes with more connections inside the set than outside. Roles based on structural similarity and communities based on proximity are fundamentally different but important complementary notions. Recently, the notion of structural roles has become increasingly important and has gained a lot of attention due to the proliferation of work on learning representations (node/edge embeddings) from graphs that preserve the notion of roles. Unfortunately, recent work has sometimes confused the notion of structural roles and communities (based on proximity) leading to misleading or incorrect claims about the capabilities of network embedding methods. As such, this article seeks to clarify the misconceptions and key differences between structural roles and communities, and formalize the general mechanisms (e.g., random walks and feature diffusion) that give rise to community- or role-based structural embeddings. We theoretically prove that embedding methods based on these mechanisms result in either community- or role-based structural embeddings. These mechanisms are typically easy to identify and can help researchers quickly determine whether a method preserves community- or role-based embeddings. Furthermore, they also serve as a basis for developing new and improved methods for community- or role-based structural embeddings. Finally, we analyze and discuss applications and data characteristics where community- or role-based embeddings are most appropriate.

中文翻译：

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网络中基于接近和结构角色的嵌入

结构角色定义了结构上相似的节点集，这些节点与集合内部的节点比外部的节点更相似，而社区定义的节点集合在集合内部比外部具有更多的连接。基于结构相似性的角色和基于接近性的社区是根本不同但重要的互补概念。最近，结构角色的概念变得越来越重要，并且由于从保留角色概念的图中学习表示（节点/边嵌入）的工作的激增而获得了很多关注。不幸的是，最近的工作有时会混淆结构角色和社区（基于邻近性）的概念，从而导致对网络嵌入方法能力的误导或错误声明。因此，本文旨在澄清结构角色和社区之间的误解和关键差异，并正式确定产生基于社区或基于角色的结构嵌入的一般机制（例如，随机游走和特征扩散）。我们从理论上证明，基于这些机制的嵌入方法会产生基于社区或基于角色的结构嵌入。这些机制通常很容易识别，并且可以帮助研究人员快速确定一种方法是否保留了基于社区或基于角色的嵌入。此外，它们还可以作为开发基于社区或角色的结构嵌入的新方法和改进方法的基础。最后，我们分析和讨论了基于社区或基于角色的嵌入最合适的应用程序和数据特征。