Random graph models for dynamic networks

We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of edges are governed by continuous-time Markov processes with rate parameters that can depend on properties of the nodes. In addition to computing equilibrium properties of these models, we demonstrate their use in data analysis and statistical inference, giving efficient algorithms for fitting them to observed network data. This allows us, for instance, to estimate the time constants of network evolution or infer community structure from temporal network data using cues embedded both in the probabilities over time that node pairs are connected by edges and in the characteristic dynamics of edge appearance and disappearance. We illustrate our methods with a selection of applications, both to computer-generated test networks and real-world examples.Comment: 15 pages, four figure

Structured Sequence Modeling with Graph Convolutional Recurrent Networks

This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by an arbitrary graph. Such structured sequences can represent series of frames in videos, spatio-temporal measurements on a network of sensors, or random walks on a vocabulary graph for natural language modeling. The proposed model combines convolutional neural networks (CNN) on graphs to identify spatial structures and RNN to find dynamic patterns. We study two possible architectures of GCRN, and apply the models to two practical problems: predicting moving MNIST data, and modeling natural language with the Penn Treebank dataset. Experiments show that exploiting simultaneously graph spatial and dynamic information about data can improve both precision and learning speed

Time-aware Random Walk Diffusion to Improve Dynamic Graph Learning

How can we augment a dynamic graph for improving the performance of dynamic graph neural networks? Graph augmentation has been widely utilized to boost the learning performance of GNN-based models. However, most existing approaches only enhance spatial structure within an input static graph by transforming the graph, and do not consider dynamics caused by time such as temporal locality, i.e., recent edges are more influential than earlier ones, which remains challenging for dynamic graph augmentation. In this work, we propose TiaRa (Time-aware Random Walk Diffusion), a novel diffusion-based method for augmenting a dynamic graph represented as a discrete-time sequence of graph snapshots. For this purpose, we first design a time-aware random walk proximity so that a surfer can walk along the time dimension as well as edges, resulting in spatially and temporally localized scores. We then derive our diffusion matrices based on the time-aware random walk, and show they become enhanced adjacency matrices that both spatial and temporal localities are augmented. Throughout extensive experiments, we demonstrate that TiaRa effectively augments a given dynamic graph, and leads to significant improvements in dynamic GNN models for various graph datasets and tasks.Comment: 16 page

A Separable Model for Dynamic Networks

Models of dynamic networks --- networks that evolve over time --- have manifold applications. We develop a discrete-time generative model for social network evolution that inherits the richness and flexibility of the class of exponential-family random graph models. The model --- a Separable Temporal ERGM (STERGM) --- facilitates separable modeling of the tie duration distributions and the structural dynamics of tie formation. We develop likelihood-based inference for the model, and provide computational algorithms for maximum likelihood estimation. We illustrate the interpretability of the model in analyzing a longitudinal network of friendship ties within a school.Comment: 28 pages (including a 4-page appendix); a substantial rewrite, with many corrections, changes in terminology, and a different analysis for the exampl

A State-Space Model for the Dynamic Random Subgraph Model

Proceedings of the 23-th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2015)International audienceIn recent years, many random graph models have been proposed to extract information from networks. The principle is to look for groups of vertices with homogenous connection profiles. Most of these models are suitable for static networks and can handle different types of edges. This work is motivated by the need of analyzing an evolving network describing email communications between employees of the Enron compagny where social positions play an important role. Therefore, in this paper, we consider the random subgraph model (RSM) which was proposed recently to model networks through latent clusters built within known partitions. Using a state space model to characterize the cluster proportions, RSM is then extended in order to deal with dynamic networks. We call the latter the dynamic random subgraph model (dRSM)