相关论文: Graph-theoretic optimization for edge consensus

Graph neural networks (GNNs) extend convolutional neural networks (CNNs) to graph-based data. A question that arises is how much performance improvement does the underlying graph structure in the GNN provide over the CNN (that ignores this…

A common issue in graph learning under the semi-supervised setting is referred to as gradient scarcity. That is, learning graphs by minimizing a loss on a subset of nodes causes edges between unlabelled nodes that are far from labelled ones…

This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…

We consider the next greedy randomized process for generating maximal H-free graphs: Given a fixed graph H and an integer n, start by taking a uniformly random permutation of the edges of the complete n-vertex graph. Then, construct an…

By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree…

Representing nodes in a network as dense vectors node embeddings is important for understanding a given network and solving many downstream tasks. In particular, for weighted homophilous graphs where similar nodes are connected with larger…

Motivated by the recent advances in the field of quantum computing, quantum systems are modelled and analyzed as networks of decentralized quantum nodes which employ distributed quantum consensus algorithms for coordination. In the…

Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…

Motivated by the exact weight perfect matching problem and recent parameterized algorithms for finding an $\ell$-th smallest perfect matching, we study structural properties of edge-weight symmetries in graphs. Recent work by El Maalouly et…

We consider network design problems in which we are given a graph and seek a min-size $2$-connected subgraph that satisfies a prescribed property. $\bullet$ In the 1-Connectivity Augmentation problem the goal is to augment a connected graph…

In this study, we analyzed the problem of accelerating the linear average consensus algorithm for complex networks. We propose a data-driven approach to tuning the weights of temporal (i.e., time-varying) networks using deep learning…

We introduce and study a generalization of conformal rigidity for graphs. A graph is $k$-conformally rigid if the uniform edge weights simultaneously maximize the sum of the $k$ smallest nontrivial Laplacian eigenvalues and minimize the sum…

We show that, for any graph optimization problem in which the feasible solutions can be expressed by a formula in monadic second-order logic describing sets of vertices or edges and in which the goal is to minimize the sum of the weights in…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…

When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when…

Solving fastest distributed consensus averaging problem (i.e., finding weights on the edges to minimize the second-largest eigenvalue modulus of the weight matrix) over networks with different topologies is one of the primary areas of…

The notion of network connectivity is used to characterize the robustness and failure tolerance of networks, with high connectivity being a desirable feature. In this paper, we develop a novel approach to the problem of identifying critical…

Graphs are a common model for complex relational data such as social networks and protein interactions, and such data can evolve over time (e.g., new friendships) and be noisy (e.g., unmeasured interactions). Link prediction aims to predict…

This paper studies the fastest distributed consensus averaging problem on branches of an arbitrary connected sensor network. In the previous works full knowledge about the sensor network's connectivity topology was required for determining…

We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…