Predicting the structure of dynamic graphs (2401.04280v2)

Abstract: Many aspects of graphs have been studied in depth. However, forecasting the structure of a graph at future time steps incorporating unseen, new nodes and edges has not gained much attention. In this paper, we present such an approach. Using a time series of graphs, we forecast graphs at future time steps. We use time series forecasting methods to predict the node degree at future time points and combine these forecasts with flux balance analysis -- a linear programming method used in biochemistry -- to obtain the structure of future graphs. We evaluate this approach using synthetic and real-world datasets and demonstrate its utility and applicability.

• The paper introduces a method that forecasts future node degrees and uses linear programming with FBA to predict evolving graph structures.
• The study shows that Formulation 2 with proportional coefficients significantly improves accuracy in capturing adjacency errors.
• The approach accommodates emerging nodes and provides practical insights for dynamic networks in communication, social media, and biochemistry.

Introduction

Machine learning and network science have long been intertwined, with network analysis providing a fertile ground for developing new learning algorithms. In recent efforts within the field of dynamic graph analysis, a novel approach has been introduced to predict the structure of future graphs in a time series, incorporating not just existing nodes and edges but also allowing for new elements. This particular paper adopts a method that merges time series forecasting with an optimization approach normally used in biochemistry, known as Flux Balance Analysis (FBA).

Predictive Approach

The core concept hinges on predicting node degrees of a graph at a future time point and using linear programming to shape this into a coherent graph structure. The methodology is split into two components: the prediction of future node degrees and the prediction of edges based on these degrees. For the degree prediction, the research harnesses conventional time series methods, assuming that the degree of each node is a temporal sequence that can be forecasted. The following phase uses FBA to create the network structure, embedding the predicted degrees as part of the constraints in an optimization problem. This method allows the accommodation of new nodes that naturally emerge in growing networks.

Methodological Insights

The approach deviates from the common tasks usually associated with dynamic graphs such as node classification or link prediction, which often necessitate some information about the graph structure at future time steps. It also distinguishes itself by taking into account the possibility of new nodes -- a scenario that closely mirrors real-world applications where networks constantly evolve.

The paper provides a clear delineation between inductive graph learning, which can generalize to unseen nodes, and incremental and dynamic graph learning, the latter focusing on updating the model while new data arrives without retraining from scratch. In terms of methodology, the paper also proposes different formulations (F1 and F2) utilizing binary and proportional coefficients (C2 and C3) and compares their efficacy in predictions.

Results and Implications

When implemented on synthetic and real-world datasets, the method shows promising results. It is most successful when using Formulation 2 (F2) coupled with proportional coefficients (C3), which handle the adjacency errors effectively. Degree cosine similarity proved to be best under Formulation 1 (F1) with proportional coefficients. In short, the researchers' technique yields estimations of future graph structures that could significantly inform areas such as communication networks, social media analysis, and biochemistry.

Closing Remarks

This paper is poised to extend the boundaries of dynamic graph prediction. By addressing both the addition of new nodes and edges fully autonomously, the method sets the stage for increasingly accurate models that can keep pace with the evolving nature of real-world networks. Future work may focus on refining the efficiency of the optimization algorithm and considering graphs where vertices or edges can be treated as interchangeable entities.