This paper proposes a metric to measure the dissimilarity between graphs that
may have a different number of nodes. The proposed metric extends the
generalised optimal subpattern assignment (GOSPA) metric, which is a metric for
sets, to graphs. The proposed graph GOSPA metric includes costs associated with
node attribute errors for properly assigned nodes, missed and false nodes and
edge mismatches between graphs. The computation of this metric is based on
finding the optimal assignments between nodes in the two graphs, with the
possibility of leaving some of the nodes unassigned. We also propose a lower
bound for the metric, which is also a metric for graphs and is computable in
polynomial time using linear programming. The metric is first derived for
undirected unweighted graphs and it is then extended to directed and weighted
graphs. The properties of the metric are demonstrated via simulated and
empirical datasets.

提出一种用于度量具有不同节点数量的图之间不相似性的测量方法，该方法基于泛化的最优子模式分配（GOSPA）度量对图进行了扩展，并包括与节点属性错误、缺失和虚假节点以及图之间的边不匹配相关的成本。该度量的计算基于在两个图之间找到节点之间的最优分配，并可能保留一些节点未分配，同时还提出了一种低界，该低界也是一种图度量，可以使用线性规划在多项式时间内计算。该度量首先针对无向无权图进行推导，然后扩展到有向和有权图，并通过模拟和实证数据集展示了其性质。

图形 GOSPA 度量：衡量不同尺寸图形之间的差异度量

Graph GOSPA metric: a metric to measure the discrepancy between graphs  of different sizes

Graphs are used widely to model complex systems, and detecting anomalies in a
graph is an important task in the analysis of complex systems. Graph anomalies
are patterns in a graph that do not conform to normal patterns expected of the
attributes and/or structures of the graph. In recent years, graph neural
networks (GNNs) have been studied extensively and have successfully performed
difficult machine learning tasks in node classification, link prediction, and
graph classification thanks to the highly expressive capability via message
passing in effectively learning graph representations. To solve the graph
anomaly detection problem, GNN-based methods leverage information about the
graph attributes (or features) and/or structures to learn to score anomalies
appropriately. In this survey, we review the recent advances made in detecting
graph anomalies using GNN models. Specifically, we summarize GNN-based methods
according to the graph type (i.e., static and dynamic), the anomaly type (i.e.,
node, edge, subgraph, and whole graph), and the network architecture (e.g.,
graph autoencoder, graph convolutional network). To the best of our knowledge,
this survey is the first comprehensive review of graph anomaly detection
methods based on GNNs.

本篇综述介绍了基于图神经网络的图形异常检测的最新进展，将这些方法总结为基于图形类型、异常类型和网络结构，并得出这是第一个基于 GNN 的综合检测图形异常方法的综述。

使用图神经网络的图异常检测：当前状态与挑战

Graph Anomaly Detection with Graph Neural Networks: Current Status and Challenges

Random walks are at the heart of many existing network embedding methods.
However, such algorithms have many limitations that arise from the use of
random walks, e.g., the features resulting from these methods are unable to
transfer to new nodes and graphs as they are tied to vertex identity. In this
work, we introduce the Role2Vec framework which uses the flexible notion of
attributed random walks, and serves as a basis for generalizing existing
methods such as DeepWalk, node2vec, and many others that leverage random walks.
Our proposed framework enables these methods to be more widely applicable for
both transductive and inductive learning as well as for use on graphs with
attributes (if available). This is achieved by learning functions that
generalize to new nodes and graphs. We show that our proposed framework is
effective with an average AUC improvement of 16.55% while requiring on average
853x less space than existing methods on a variety of graphs.

本文介绍了使用 Role2Vec 框架基于属性随机游走的方法来在图形数据分析中实现广义深度学习和节点表示学习，并取得了较好的效果和泛化能力。