Related papers: Emergent hierarchy through conductance-based node …

A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a…

Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or…

Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior while others behave erratically. Predicting the emergence of these clusters and understanding the…

We propose a novel network formation game that explains the emergence of various hierarchical structures in groups where self-interested or utility-maximizing individuals decide to establish or severe relationships of authority or…

There is a commonality among contagious diseases, tweets, urban crimes, nuclear reactions, and neuronal firings that past events facilitate the future occurrence of events. The spread of events has been extensively studied such that the…

Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…

We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…

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…

The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…

Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…

We started with a knowledge graph of connected entities and descriptive properties of those entities, from which, a hierarchical representation of the knowledge graph is derived. Using a graphical, energy-based neural network, we are able…

Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…

There is plenty of theoretical and empirical evidence that depth of neural networks is a crucial ingredient for their success. However, network training becomes more difficult with increasing depth and training of very deep networks remains…

We define gradient networks as directed graphs formed by local gradients of a scalar field distributed on the nodes of a substrate network G. We derive an exact expression for the in-degree distribution of the gradient network when the…

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…

We show that, in contrast to classical random graph models, many real-world complex systems -- including a variety of biological regulatory networks and technological networks such as the internet -- spontaneously self-organize to a richly…

We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…

In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…

It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…

We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism…