skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Thursday, October 10 until 2:00 AM ET on Friday, October 11 due to maintenance. We apologize for the inconvenience.


Title: On the Power of Edge Independent Graph Models
Why do many modern neural-network-based graph generative models fail to reproduce typical real-world network characteristics, such as high triangle density? In this work we study the limitations of edge independent random graph models, in which each edge is added to the graph independently with some probability. Such models include both the classic Erdös-Rényi and stochastic block models, as well as modern generative models such as NetGAN, variational graph autoencoders, and CELL. We prove that subject to a bounded overlap condition, which ensures that the model does not simply memorize a single graph, edge independent models are inherently limited in their ability to generate graphs with high triangle and other subgraph densities. Notably, such high densities are known to appear in real-world social networks and other graphs. We complement our negative results with a simple generative model that balances overlap and accuracy, performing comparably to more complex models in reconstructing many graph statistics.  more » « less
Award ID(s):
1763618
NSF-PAR ID:
10355852
Author(s) / Creator(s):
Date Published:
Journal Name:
Conference on Neural Information Processing Systems (NeurIPS)
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Lateral movement is a key stage of system compromise used by advanced persistent threats. Detecting it is no simple task. When network host logs are abstracted into discrete temporal graphs, the problem can be reframed as anomalous edge detection in an evolving network. Research in modern deep graph learning techniques has produced many creative and complicated models for this task. However, as is the case in many machine learning fields, the generality of models is of paramount importance for accuracy and scalability during training and inference. In this article, we propose a formalized approach to this problem with a framework we call Euler . It consists of a model-agnostic graph neural network stacked upon a model-agnostic sequence encoding layer such as a recurrent neural network. Models built according to the Euler framework can easily distribute their graph convolutional layers across multiple machines for large performance improvements. Additionally, we demonstrate that Euler -based models are as good, or better, than every state-of-the-art approach to anomalous link detection and prediction that we tested. As anomaly-based intrusion detection systems, our models efficiently identified anomalous connections between entities with high precision and outperformed all other unsupervised techniques for anomalous lateral movement detection. Additionally, we show that as a piece of a larger anomaly detection pipeline, Euler models perform well enough for use in real-world systems. With more advanced, yet still lightweight, alerting mechanisms ingesting the embeddings produced by Euler models, precision is boosted from 0.243, to 0.986 on real-world network traffic. 
    more » « less
  2. Counting and finding triangles in graphs is often used in real-world analytics to characterize cohesiveness and identify communities in graphs. In this paper, we propose the novel concept of a cover-edge set that can be used to find triangles more efficiently. We use a breadth-first search (BFS) to quickly generate a compact cover-edge set. Novel sequential and parallel triangle counting algorithms are presented that employ cover-edge sets. The sequential algorithm avoids unnecessary triangle-checking operations, and the parallel algorithm is communication-efficient. The parallel algorithm can asymptotically reduce communication on massive graphs such as from real social networks and synthetic graphs from the Graph500 Benchmark. In our estimate from massive-scale Graph500 graphs, our new parallel algorithm can reduce the communication on a scale 36 graph by 1156x and on a scale 42 graph by 2368x. 
    more » « less
  3. Diffusion-based graph generative models are effective in generating high-quality small graphs. However, it is hard to scale them to large graphs that contain thousands of nodes. In this work, we propose EDGE, a new diffusion-based graph generative model that addresses generative tasks for large graphs. The model is developed by reversing a discrete diffusion process that randomly removes edges until obtaining an empty graph. It leverages graph sparsity in the diffusion process to improve computational efficiency. In particular, EDGE only focuses on a small portion of graph nodes and only adds edges between these nodes. Without compromising modeling ability, it makes much fewer edge predictions than previous diffusion-based generative models. Furthermore, EDGE can explicitly model the node degrees of training graphs and then gain performance improvement in capturing graph statistics. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by the proposed model have graph statistics more similar to those of training graphs. 
    more » « less
  4. Diffusion-based graph generative models are effective in generating high-quality small graphs. However, it is hard to scale them to large graphs that contain thousands of nodes. In this work, we propose EDGE, a new diffusion-based graph generative model that addresses generative tasks for large graphs. The model is developed by reversing a discrete diffusion process that randomly removes edges until obtaining an empty graph. It leverages graph sparsity in the diffusion process to improve computational efficiency. In particular, EDGE only focuses on a small portion of graph nodes and only adds edges between these nodes. Without compromising modeling ability, it makes much fewer edge predictions than previous diffusion-based generative models. Furthermore, EDGE can explicitly model the node degrees of training graphs and then gain performance improvement in capturing graph statistics. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by the proposed model have graph statistics more similar to those of training graphs. 
    more » « less
  5. null (Ed.)
    Low-dimensional embeddings, from classical spectral embeddings to modern neural-net-inspired methods, are a cornerstone in the modeling and analysis of complex networks. Recent work by Seshadhri et al. (PNAS 2020) suggests that such embeddings cannot capture local structure arising in complex networks. In particular, they show that any network generated from a natural low-dimensional model cannot be both sparse and have high triangle density (high clustering coefficient), two hallmark properties of many real-world networks. In this work we show that the results of Seshadhri et al. are intimately connected to the model they use rather than the low-dimensional structure of complex networks. Specifically, we prove that a minor relaxation of their model can generate sparse graphs with high triangle density. Surprisingly, we show that this same model leads to exact low-dimensional factorizations of many real-world networks. We give a simple algorithm based on logistic principal component analysis (LPCA) that succeeds in finding such exact embeddings. Finally, we perform a large number of experiments that verify the ability of very low-dimensional embeddings to capture local structure in real-world networks. 
    more » « less