Related papers: A General Solution for Network Models with Pairwis…
Higher-order interactions play a key role for the stability and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of…
Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes…
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…
People organize in groups and contagions spread across them. A simple process, but complex to model due to dynamical correlations within groups and between groups. Groups can also change as agents join and leave them to avoid infection. To…
Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…
The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve…
The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…
We consider the count of subgraphs with an arbitrary configuration of endpoints in the random-connection model based on a Poisson point process on ${\Bbb R}^d$. We present combinatorial expressions for the computation of the cumulants and…
Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions cannot be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
This paper provides a necessary and sufficient condition for a random network with nodes Poissonly distributed on a unit square and a pair of nodes directly connected following a generic random connection model to be asymptotically almost…
Graph-theoretic methods have seen wide use throughout the literature on multi-agent control and optimization. When communications are intermittent and unpredictable, such networks have been modeled using random communication graphs. When…
Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with…
Pairwise models like the Ising model or the generalized Potts model have found many successful applications in fields like physics, biology, and economics. Closely connected is the problem of inverse statistical mechanics, where the goal is…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…