Community detection and graph clustering are essential for unsupervised data
exploration and understanding the high-level organisation of networked systems.
Recently, graph clustering has been highlighted as an under-explored primary
task for graph neural networks. While hierarchical graph pooling has been shown
to improve performance in graph and node classification tasks, it performs
poorly in identifying meaningful clusters. Community detection has a long
history in network science, but typically relies on optimising objective
functions with custom-tailored search algorithms, not leveraging recent
advances in deep learning, particularly from graph neural networks. In this
paper, we narrow this gap between the deep learning and network science
communities. We consider the map equation, an information-theoretic objective
function for community detection. Expressing it in a fully differentiable
tensor form that produces soft cluster assignments, we optimise the map
equation with deep learning through gradient descent. More specifically, the
reformulated map equation is a loss function compatible with any graph neural
network architecture, enabling flexible clustering and graph pooling that
clusters both graph structure and data features in an end-to-end way,
automatically finding an optimum number of clusters without explicit
regularisation. We evaluate our approach experimentally using different neural
network architectures for unsupervised clustering in synthetic and real data.
Our results show that our approach achieves competitive performance against
baselines, naturally detects overlapping communities, and avoids
over-partitioning sparse graphs.

通过梯度下降优化可完全可微的张量形式的映射方程，以深度学习为基础的图神经网络在社区检测和图聚类任务上取得了具有竞争力的性能，同时能够自动确定最优的聚类数目，并能够避免过分划分稀疏图。

地图方程转为神经网络

The Map Equation Goes Neural

Many real-world networks are so large that we must simplify their structure
before we can extract useful information about the systems they represent. As
the tools for doing these simplifications proliferate within the network
literature, researchers would benefit from some guidelines about which of the
so-called community detection algorithms are most appropriate for the
structures they are studying and the questions they are asking. Here we show
that different methods highlight different aspects of a network's structure and
that the the sort of information that we seek to extract about the system must
guide us in our decision. For example, many community detection algorithms,
including the popular modularity maximization approach, infer module
assignments from an underlying model of the network formation process. However,
we are not always as interested in how a system's network structure was formed,
as we are in how a network's extant structure influences the system's behavior.
To see how structure influences current behavior, we will recognize that links
in a network induce movement across the network and result in system-wide
interdependence. In doing so, we explicitly acknowledge that most networks
carry flow. To highlight and simplify the network structure with respect to
this flow, we use the map equation. We present an intuitive derivation of this
flow-based and information-theoretic method and provide an interactive on-line
application that anyone can use to explore the mechanics of the map equation.
We also describe an algorithm and provide source code to efficiently decompose
large weighted and directed networks based on the map equation.

研究不同社区检测算法对于网络结构的影响及其应用，介绍流动与信息论相结合的 Map Equation 方法并提供在线应用及分解算法。