Related papers: Growth principles of natural hypergraphs

Hypergraphs are higher-order networks that capture the interactions between two or more nodes. Hypergraphs can always be represented by factor graphs, i.e. bipartite networks between nodes and factor nodes (representing groups of nodes).…

Hypergraphs provide a fundamental framework for representing complex systems involving interactions among three or more entities. As empirical hypergraphs grow in size, characterizing their structural properties becomes increasingly…

Many complex systems are characterized by broad distributions capturing, for example, the size of firms, the population of cities or the degree distribution of complex networks. Typically this feature is explained by means of a preferential…

We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic…

Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…

Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…

Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…

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…

The discovery and analysis of network patterns are central to the scientific enterprise. In the present work, we developed and evaluated a new approach that learns the building blocks of graphs that can be used to understand and generate…

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…

We propose a new preferential attachment-based network growth model in order to explain two properties of growing networks: (1) the power-law growth of node degrees and (2) the decay of node relevance. In preferential attachment models, the…

We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…

Graph representations of solid state materials that encode only interatomic distance lack geometrical resolution, resulting in degenerate representations that may map distinct structures to equivalent graphs. Here we propose a hypergraph…

Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…

We propose a growing network model that consists of two tunable mechanisms: growth by merging modules which are represented as complete graphs and a fitness-driven preferential attachment. Our model exhibits the three prominent statistical…

The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…