相关论文: Can one see the shape of a network?

We have developed different network approaches to analyze complex patterns of frictional interfaces (contact area developments). Network theory is a fundamental tool for the modern understanding of complex systems in which, by a simple…

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…

Given a valued graph, where both the nodes and the edges of the graph are associated with one or several values, any network function for a given node must be defined in terms of that node and its connected nodes in the graph. Generally,…

We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…

Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street…

The graph theoretic properties of the clustering coefficient, characteristic (or average) path length, global and local efficiency, provide valuable information regarding the structure of a graph. These four properties have applications to…

The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…

In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…

The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network…

Graph neural network (GNN) has been demonstrated powerful in modeling graph-structured data. However, despite many successful cases of applying GNNs to various graph classification and prediction tasks, whether the graph geometrical…

Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes…

We present a collection of results on the evolution by curvature of networks of planar curves. We discuss in particular the existence of a solution and the analysis of singularities.

In the framework of on nonassociative geometry, we introduce a new effective model that extends the statistical treatment of complex networks with hidden geometry. The small-world property of the network is controlled by nonlocal curvature…

It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability…

Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes…

Understanding key structural properties of large scale networks are crucial for analyzing and optimizing their performance, and improving their reliability and security. Here we show that these networks possess a previously unnoticed…

In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…

A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described. Traditionally this has been taken to mean that a graph network must be equivariant to node…

Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…

We define notions of local topological convergence and local geometric convergence for embedded graphs in $\mathbb{R}^n,$ and study their properties. The former is related to Benjamini-Schramm convergence, and the latter to weak convergence…