Related papers: Growing scale-free simplices
The scale-free (SF) structure that commonly appears in many complex networks is one of the hot topics related to social, biological, and information sciences. The self-organized generation mechanisms are expected to be useful for efficient…
Recent years have seen a growing interest in the modeling and simulation of social networks to understand several social phenomena. Two important classes of networks, small world and scale free networks have gained a lot of research…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
Scale-free networks are ubiquitous in social, biological and technological networked systems. Dynamic Scale-free networks and their synchronizations are important to understand and predict the behavior of social, biological and…
Recently there have been a tremendous interest in models of networks with a power-law distribution of degree -- so called "scale-free networks." It has been observed that such networks, normally, have extremely short path-lengths, scaling…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the…
Despite being a source of rich information, graphs are limited to pairwise interactions. However, several real-world networks such as social networks, neuronal networks, etc., involve interactions between more than two nodes. Simplicial…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
Real-world networks grow over time; statistical models based on node exchangeability are not appropriate. Instead of constraining the structure of the \textit{distribution} of edges, we propose that the relevant symmetries refer to the…
We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not…
Cascades arise in many contexts (e.g., neuronal avalanches, social contagions, and system failures). Despite evidence that propagations often involve higher-order dependencies, cascade theory has largely focused on models with…
We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
Many real-world complex systems such as social, biological, information as well as technological systems results of a decentralized and unplanned evolution which leads to a common structuration. Irrespective of their origin, these so-called…
We extend the standard scale-free network model to include a ``triad formation step''. We analyze the geometric properties of networks generated by this algorithm both analytically and by numerical calculations, and find that our model…
In the paper, we present an incremental approach in the construction of scale free networks with hidden variables. The work arises from the necessity to generate that type of networks with a given number of links instead of obtaining a…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…