相关论文: Metric tree-like structures in real-life networks:…

The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…

Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…

This paper addresses the basic question of how well can a tree approximate distances of a metric space or a graph. Given a graph, the problem of constructing a spanning tree in a graph which strongly preserves distances in the graph is a…

Data-driven analysis of large social networks has attracted a great deal of research interest. In this paper, we investigate 120 real social networks and their measurement-calibrated synthetic counterparts generated by four well-known…

We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…

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…

There are hierarchical characteristics in the network and how to effectively reveal the hierarchical characteristics in the network is a problem in the research of network structure. If a node is assigned to the community to which it…

Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…

Since they became observable, neuron morphologies have been informally compared with biological trees but they are studied by distinct communities, neuroscientists, and ecologists. The apparent structural similarity suggests there may be…

Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and…

Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…

We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…

Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or…

Phylogenetic trees are often constructed by using a metric on the set of taxa that label the leaves of the tree. While there are a number of methods for constructing a tree using a given metric, such trees will only display the metric if it…

Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…

A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…

Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to…

The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is…

Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…

The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…