Related papers: Forman curvature for complex networks

Graph neural networks (GNNs) have achieved great success in many graph-based tasks. Much work is dedicated to empowering GNNs with the adaptive locality ability, which enables measuring the importance of neighboring nodes to the target node…

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…

Many complex networks in the real world have community structures -- groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.…

Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are many measures available and it is speculated that many encode similar information. We give an explicit non-linear…

Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…

Based on two classical notions of curvature for curves in general metric spaces, namely the Menger and Haantjes curvatures, we introduce new definitions of sectional, Ricci and scalar curvature for networks and their higher dimensional…

Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which node-removal order has the greatest impact on the network structure? We approach this well-known problem for the first time…

In contrast to graph-based models for complex networks, hypergraphs are more general structures going beyond binary relations of graphs. For graphs, statistics gauging different aspects of their structures have been devised and there is…

Robustness in response to unexpected events is always desirable for real-world networks. To improve the robustness of any networked system, it is important to analyze vulnerability to external perturbation such as random failures or…

In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…

Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…

Forman-Ricci curvature (FRC) is a potent and powerful tool for analysing empirical networks, as the distribution of the curvature values can identify structural information that is not readily detected by other geometrical methods.…

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…

Many naturally occurring networks have a power-law degree distribution as well as a non-zero degree correlation. Despite this, most studies analyzing the robustness to random node-deletion and vulnerability to targeted node-deletion have…

In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…

Ricci curvature and Ricci flow have proven to be powerful tools for analyzing the geometry of discrete structures, particularly on undirected graphs, where they have been applied to tasks ranging from community detection to graph…

The complexity of financial markets arise from the strategic interactions among agents trading stocks, which manifest in the form of vibrant correlation patterns among stock prices. Over the past few decades, complex financial markets have…

Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…

The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…

Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…