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Unrolled networks have become prevalent in various computer vision and imaging tasks. Although they have demonstrated remarkable efficacy in solving specific computer vision and computational imaging tasks, their adaptation to other…

Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…

Many applications in network science have recently been discovered for the "curvature" of a network, but there is no consensus on the definition for this term. A common approach in these applications is to derive from the curvature either a…

The essential graph is a distinguished member of a Markov equivalence class of AMP chain graphs. However, the directed edges in the essential graph are not necessarily strong or invariant, i.e. they may not be shared by every member of the…

Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…

Several problems such as network intrusion, community detection, and disease outbreak can be described by observations attributed to nodes or edges of a graph. In these applications presence of intrusion, community or disease outbreak is…

This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models.…

Several large scale networks, such as the backbone of the Internet, have been observed to behave like convex Riemannian manifolds of negative curvature. In particular, this paradigm explains the observed existence, for networks of this…

With the recent popularity of graphical clustering methods, there has been an increased focus on the information between samples. We show how learning cluster structure using edge features naturally and simultaneously determines the most…

We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and…

Shape graphs are complex geometrical structures commonly found in biological and anatomical systems. A shape graph is a collection of nodes, some connected by curvilinear edges with arbitrary shapes. Their high complexity stems from the…

Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…

Finding dense bipartite subgraphs and detecting the relations among them is an important problem for affiliation networks that arise in a range of domains, such as social network analysis, word-document clustering, the science of science,…

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…

Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…

Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…

Planar drawings of graphs tend to be favored over non-planar drawings. Testing planarity and creating a planar layout of a planar graph can be done in linear time. However, creating readable drawings of nearly planar graphs remains a…

Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…

The paper aims to investigate relevant computational issues of deep neural network architectures with an eye to the interaction between the optimization algorithm and the classification performance. In particular, we aim to analyze the…