Related papers: Network-Based Vertex Dissolution
We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
The weak minor G of a graph G is the graph obtained from G by a sequence of edge-contraction operations on G. A weak-minor-closed family of upper embeddable graphs is a set G of upper embeddable graphs that for each graph G in G, every weak…
Partitioning an input graph over a set of workers is a complex operation. Objectives are twofold: split the work evenly, so that every worker gets an equal share, and minimize edge cut to achieve a good work locality (i.e. workers can work…
(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…
One of the principal goals of graph modeling is to capture the building blocks of network data in order to study various physical and natural phenomena. Recent work at the intersection of formal language theory and graph theory has explored…
Graph partitioning problems are a central topic of study in algorithms and complexity theory. Edge expansion and vertex expansion, two popular graph partitioning objectives, seek a $2$-partition of the vertex set of the graph that minimizes…
Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…
We introduce the graphlet decomposition of a weighted network, which encodes a notion of social information based on social structure. We develop a scalable inference algorithm, which combines EM with Bron-Kerbosch in a novel fashion, for…
We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged.…
Graph vertex ordering is widely employed in spatial data analysis, especially in urban analytics, where street graphs serve as spatial discretization for modeling and simulation. It is also crucial for visualization, as many methods require…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Network embedding is an important step in many different computations based on graph data. However, existing approaches are limited to small or middle size graphs with fewer than a million edges. In practice, web or social network graphs…
Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges…
Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
In recent years, machine learning and deep learning approaches such as artificial neural networks have gained in popularity for the resolution of automatic puzzle resolution problems. Indeed, these methods are able to extract high-level…
Our aim here is to address the problem of decomposing a whole network into a minimal number of ego-centered subnetworks. For this purpose, the network egos are picked out as the members of a minimum dominating set of the network. However,…
The urban networks of London and New York City are investigated as directed graphs within the paradigm of graph percolation. It has been recently observed that urban networks show a critical percolation transition when a fraction of edges…
Finding maximum-weight independent sets in graphs is an important NP-hard optimization problem. Given a vertex-weighted graph $G$, the task is to find a subset of pairwise non-adjacent vertices of $G$ with maximum weight. Most recently…