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Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing…

The task of representing entire graphs has seen a surge of prominent results, mainly due to learning convolutional neural networks (CNNs) on graph-structured data. While CNNs demonstrate state-of-the-art performance in graph classification…

This study investigates the robustness of graph embedding methods for community detection in the face of network perturbations, specifically edge deletions. Graph embedding techniques, which represent nodes as low-dimensional vectors, are…

The stochastic block model (SBM) with two communities, or equivalently the planted bisection model, is a popular model of random graph exhibiting a cluster behaviour. In the symmetric case, the graph has two equally sized clusters and…

With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. Stochastic block model constitutes a classical…

Recent research on network embedding in hyperbolic space have proven successful in several applications. However, nodes in real world networks tend to interact through several distinct channels. Simple aggregation or ignorance of this…

Statistical inference on graphs often proceeds via spectral methods involving low-dimensional embeddings of matrix-valued graph representations, such as the graph Laplacian or adjacency matrix. In this paper, we analyze the asymptotic…

Block coordinate descent is an optimization paradigm that iteratively updates one block of variables at a time, making it quite amenable to big data applications due to its scalability and performance. Its convergence behavior has been…

Graph embedding methods represent nodes in a continuous vector space, preserving information from the graph (e.g. by sampling random walks). There are many hyper-parameters to these methods (such as random walk length) which have to be…

The stochastic block model (SBM) is a random graph model in which the edges are generated according to the underlying cluster structure on the vertices. The (ferromagnetic) Ising model, on the other hand, assigns $\pm 1$ labels to vertices…

The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study…

Graph representation learning (also called graph embeddings) is a popular technique for incorporating network structure into machine learning models. Unsupervised graph embedding methods aim to capture graph structure by learning a…

An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…

This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…

Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…

Random walks are at the heart of many existing network embedding methods. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to transfer to new…

The Stochastic Block Model (SBM) is a widely used random graph model for networks with communities. Despite the recent burst of interest in recovering communities in the SBM from statistical and computational points of view, there are still…

Neighbor Embedding (NE) aims to preserve pairwise similarities between data items and has been shown to yield an effective principle for data visualization. However, even the best existing NE methods such as Stochastic Neighbor Embedding…

Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and…