Graph-based data present unique challenges and opportunities for machine learning. Graph Neural Networks (GNNs), and especially those algorithms that capture graph topology through message passing for neighborhood aggregation, have been a leading solution. However, these networks often require substantial computational resources and may not optimally leverage the information contained in the graph’s topology, particularly for large-scale or complex graphs.We propose Topology Coordinate Neural Network (TCNN) and Directional Virtual Coordinate Neural Network (DVCNN) as novel and efficient alternatives to message passing GNNs, that directly leverage the graph’s topology, sidestepping the computational challenges presented by competing algorithms. Our proposed methods can be viewed as a reprise of classic techniques for graph embedding for neural network feature engineering, but they are novel in that our embedding techniques leverage ideas in Graph Coordinates (GC) that are lacking in current practice.Experimental results, benchmarked against the Open Graph Benchmark Leaderboard, demonstrate that TCNN and DVCNN achieve competitive or superior performance to message passing GNNs. For similar levels of accuracy and ROC-AUC, TCNN and DVCNN need far fewer trainable parameters than contenders of the OGBN Leaderboard. The proposed TCNN architecture requires fewer parameters than any neural network method currently listed in the OGBN Leaderboard for both OGBN-Proteins and OGBN-Products datasets. Conversely, our methods achieve higher performance for a similar number of trainable parameters. These results hold across diverse datasets and edge features, underscoring the robustness and generalizability of our methods. By providing an efficient and effective alternative to message passing GNNs, our work expands the toolbox of techniques for graph-based machine learning. A significantly lower number of tunable parameters for a given evaluation metric makes TCNN and DVCNN especially attractive for resource limited IoT/mobile devices and for reducing power consumption of ML models.

In this paper, we propose a novel method to make distance predictions in real-world social networks. As predicting missing distances is a difficult problem, we take a two-stage approach. Structural parameters for families of synthetic networks are first estimated from a small set of measurements of a real-world network and these synthetic networks are then used to pre-train the predictive neural networks. Since our model first searches for the most suitable synthetic graph parameters which can be used as an “oracle” to create arbitrarily large training data sets, we call our approach “Oracle Search Pre-training” (OSP). Such an approach enables us to evaluate the robustness of the autoencoder to artificial training data while making predictions on real-world social networks.For example, many real-world networks exhibit a Power law structure in their node degree distribution, so a Power law model can provide a foundation for the desired oracle to generate synthetic pre-training networks, if the appropriate Power law graph parameters can be estimated. Accordingly, we conduct experiments on real-world Facebook, Email, and Train Bombing networks and show that OSP outperforms models without pre-training, models pre-trained with inaccurate parameters, and other distance prediction schemes such as Low-rank Matrix Completion. In particular, we achieve a prediction error of less than one hop with only 1% of sampled distances from the social network. OSP can be easily extended to other domains such as random networks by choosing an appropriate model to generate synthetic training data, and therefore promises to impact many different network learning problems.

This paper proposes the use of graph pattern matching for investigative graph search, which is the process of searching for and prioritizing persons of interest who may exhibit part or all of a pattern of suspicious behaviors or connections. While there are a variety of applications, our principal motivation is to aid law enforcement in the detection of homegrown violent extremists. We introduce investigative simulation, which consists of several necessary extensions to the existing dual simulation graph pattern matching scheme in order to make it appropriate for intelligence analysts and law enforcement officials. Specifically, we impose a categorical label structure on nodes consistent with the nature of indicators in investigations, as well as prune or complete search results to ensure sensibility and usefulness of partial matches to analysts. Lastly, we introduce a natural top-k ranking scheme that can help analysts prioritize investigative efforts. We demonstrate performance of investigative simulation on a real-world large dataset.

Investigative graph search is the process of searching for and prioritizing entities of interest that may exhibit part or all of a pattern of attributes or connections for a latent behavior. In this work we formulate a related sub-problem of determining the pattern matching trajectories of such entities. The goal is to not only provide analysts with the ability to find full or partial matches against a query pattern, but also a means to quantify the pace of the appearance of the indicators. This technology has a variety of potential applications such as aiding in the detection of homegrown violent extremists before they carry out acts of domestic terrorism, detecting signs for post-traumatic stress in veterans, or tracking potential customer activities and experiences along a consumer journey. We propose a vectorized graph pattern matching approach that calculates the multi-hop class similarities between nodes in query and data graphs over time. By tracking partial match trajectories, we provide another dimension of analysis in investigative graph searches to highlight entities on a pathway towards a pattern of a latent behavior. We demonstrate the performance of our approach on a real-world BlogCatalog dataset of over 470K nodes and 4 million edges, where 98.56% of nodes and 99.65% of edges were filtered out with preprocessing steps, and successfully detected the trajectory of the top 1,327 nodes towards a query pattern.