Multi-MotifGAN (MMGAN): Motif-targeted Graph Generation and Prediction

Generative graph models create instances of graphs that mimic the properties of real-world networks. Generative models are successful at retaining pairwise associations in the underlying networks but often fail to capture higher-order connectivity patterns known as network motifs. Different types of graphs contain different network motifs, an example of which are triangles that often arise in social and biological networks. It is hence vital to capture these higher-order structures to simulate real-world networks accurately. We propose Multi-MotifGAN (MMGAN), a motif-targeted Generative Adversarial Network (GAN) that generalizes the benchmark NetGAN approach. The generalization consists of combining multiple biased random walks, each of which captures a different motif structure. MMGAN outperforms NetGAN at creating new graphs that accurately reflect the network motif statistics of input graphs such as Citeseer, Cora and Facebook.

Multi-View Graph Embedding Using Randomized Shortest Paths

Real-world data sets often provide multiple types of information about the same set of entities. This data is well represented by multi-view graphs, which consist of several distinct sets of edges over the same nodes. These can be used to analyze how entities interact from different viewpoints. Combining multiple views improves the quality of inferences drawn from the underlying data, which has increased interest in developing efficient multi-view graph embedding methods. We propose an algorithm, C-RSP, that generates a common (C) embedding of a multi-view graph using Randomized Shortest Paths (RSP). This algorithm generates a dissimilarity measure between nodes by minimizing the expected cost of a random walk between any two nodes across all views of a multi-view graph, in doing so encoding both the local and global structure of the graph. We test C-RSP on both real and synthetic data and show that it outperforms benchmark algorithms at embedding and clustering tasks while remaining computationally efficient.

Faster Clustering via Non-Backtracking Random Walks

This paper presents VEC-NBT, a variation on the unsupervised graph clustering technique VEC, which improves upon the performance of the original algorithm significantly for sparse graphs. VEC employs a novel application of the state-of-the-art word2vec model to embed a graph in Euclidean space via random walks on the nodes of the graph. In VEC-NBT, we modify the original algorithm to use a non-backtracking random walk instead of the normal backtracking random walk used in VEC. We introduce a modification to a non-backtracking random walk, which we call a begrudgingly-backtracking random walk, and show empirically that using this model of random walks for VEC-NBT requires shorter walks on the graph to obtain results with comparable or greater accuracy than VEC, especially for sparser graphs.