Recently, there has been an interest in embedding networks in hyperbolic
space, since hyperbolic space has been shown to work well in capturing
graph/network structure as it can naturally reflect some properties of complex
networks. However, the work on network embedding in hyperbolic space has been
focused on microscopic node embedding. In this work, we are the first to
present a framework to embed the structural roles of nodes into hyperbolic
space. Our framework extends struct2vec, a well-known structural role
preserving embedding method, by moving it to a hyperboloid model. We evaluated
our method on four real-world and one synthetic network. Our results show that
hyperbolic space is more effective than euclidean space in learning latent
representations for the structural role of nodes.

本文探讨网络嵌入在双曲空间中的应用，提出一种新的框架可以在超空间嵌入节点的结构角色，并在实际网络中进行了评估，结果表明超空间比欧几里得空间更有效地学习节点的结构表示。

将节点结构角色身份嵌入到双曲空间中

Embedding Node Structural Role Identity into Hyperbolic Space

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 paper
seeks to clarify the misconceptions and key differences between structural
roles and communities, and formalize the general mechanisms (e.g., random
walks, 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.

本篇论文介绍了结构角色和社群的概念，阐明了二者的本质区别，探讨了通过随机游走、特征扩散等机制实现社群或角色结构嵌入的方法，并分析了适用于社群或角色结构嵌入的应用和数据特征。

关于网络中的接近性和结构角色嵌入：误解、技术和应用

On Proximity and Structural Role-based Embeddings in Networks:  Misconceptions, Techniques, and Applications

Nodes residing in different parts of a graph can have similar structural
roles within their local network topology. The identification of such roles
provides key insight into the organization of networks and can be used for a
variety of machine learning tasks. However, learning structural representations
of nodes is a challenging problem, and it has typically involved manually
specifying and tailoring topological features for each node. In this paper, we
develop GraphWave, a method that represents each node's network neighborhood
via a low-dimensional embedding by leveraging heat wavelet diffusion patterns.
Instead of training on hand-selected features, GraphWave learns these
embeddings in an unsupervised way. We mathematically prove that nodes with
similar network neighborhoods will have similar GraphWave embeddings even
though these nodes may reside in very different parts of the network, and our
method scales linearly with the number of edges. Experiments in a variety of
different settings demonstrate GraphWave's real-world potential for capturing
structural roles in networks, and our approach outperforms existing
state-of-the-art baselines in every experiment, by as much as 137%.

本文介绍了 GraphWave 方法，通过利用热波中的扩散模式，表示每个节点的网络邻域，并以无监督的方式学习这些嵌入。本文证明，具有类似网络邻域的节点将具有类似的 GraphWave 嵌入，即使这些节点可能位于网络的非常不同的部分，该方法在捕捉网络中的结构角色方面有着很高的潜力，并且在实验中表现出优秀的性能，超过了现有的所有基线方法，最高达到 137%。