相关论文: The ultrametric backbone is the union of all minim…

The weight of the minimum spanning tree in a complete weighted graph with random edge weights is a well-known problem. For various classes of distributions, it is proved that the weight of the minimum spanning tree tends to a constant,…

Understanding the structure of minor-free metrics, namely shortest path metrics obtained over a weighted graph excluding a fixed minor, has been an important research direction since the fundamental work of Robertson and Seymour. A…

An undirected graphical model is a joint probability distribution defined on an undirected graph G*, where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among…

We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights…

The Pathwidth Theorem states that if a class of graphs has unbounded pathwidth, then it contains all trees as graph minors. We prove a similar result for dense graphs. More precisely, we give a finite family of tree-like patterns and prove…

In a strongly connected graph $G = (V,E)$, a cut arc (also called strong bridge) is an arc $e \in E$ whose removal makes the graph no longer strongly connected. Equivalently, there exist $u,v \in V$, such that all $u$-$v$ walks contain $e$.…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

Treewidth is a graph parameter that plays a fundamental role in several structural and algorithmic results. We study the problem of decomposing a given graph $G$ into node-disjoint subgraphs, where each subgraph has sufficiently large…

With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…

We attempt to shed new light on the notion of 'tree-like' metric spaces by focusing on an approach that does not use the four-point condition. Our key question is: Given metric space $M$ on $n$ points, when does a fully labelled…

In recent years there has been a paradigm shift from the study of local task-related activation to the organization and functioning of large-scale functional and structural brain networks. However, a long-standing challenge in this…

Many multivariate data such as social and biological data exhibit complex dependencies that are best characterized by graphs. Unlike sequential data, graphs are, in general, unordered structures. This means we can no longer use classic,…

Networks are powerful instruments to study complex phenomena, but they become hard to analyze in data that contain noise. Network backbones provide a tool to extract the latent structure from noisy networks by pruning non-salient edges. We…

We provide new results on the structure of optimal transportation networks obtained as minimizers of an energy cost functional consisting of a kinetic (pumping) and material (metabolic) cost terms, constrained by a local mass conservation…

In this paper, we investigate the problem of network backbone discovery. In complex systems, a "backbone" takes a central role in carrying out the system functionality and carries the bulk of system traffic. It also both simplifies and…

We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…

Graph-structured data arise ubiquitously in many application domains. A fundamental problem is to quantify their similarities. Graph kernels are often used for this purpose, which decompose graphs into substructures and compare these…

In established network architectures, shortcut connections are often used to take the outputs of earlier layers as additional inputs to later layers. Despite the extraordinary effectiveness of shortcuts, there remain open questions on the…

Spanning trees are an important primitive in many data analysis tasks, when a data set needs to be summarized in terms of its "skeleton", or when a tree-shaped graph over all observations is required for downstream processing. Popular…

Computing a Euclidean minimum spanning tree of a set of points is a seminal problem in computational geometry and geometric graph theory. We combine it with another classical problem in graph drawing, namely computing a monotone geometric…