Related papers: Euclidean versus hyperbolic congestion in idealize…

We investigate the impact the negative curvature has on the traffic congestion in large-scale networks. We prove that every Gromov hyperbolic network $G$ admits a core, thus answering in the positive a conjecture by Jonckheere, Lou,…

In this work we study the asymptotic traffic flow in Gromov's hyperbolic graphs when the traffic decays exponentially with the distance. We prove that under general conditions, there exists a phase transition between local and global…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

Congestion and extreme events in transportation networks are emergent phenomena with significant socio-economic implications. In this work, we study congestion and extreme event properties on real urban street (planar) networks drawn from…

Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link…

The congestion formation on a urban road network is one of the key issue for the development of a sustainable mobility in the future smart cities. In this work we propose a reductionist approach studying the stationary states of a simple…

Maximal clique enumeration appears in various real-world networks, such as social networks and protein-protein interaction networks for different applications. For general graph inputs, the number of maximal cliques can be up to…

Several large scale networks, such as the backbone of the Internet, have been observed to behave like convex Riemannian manifolds of negative curvature. In particular, this paradigm explains the observed existence, for networks of this…

Various empirical and theoretical studies indicate that cumulative network traffic is a Gaussian process. However, depending on whether the intensity at which sessions are initiated is large or small relative to the session duration tail,…

We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…

Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods…

In this work we study the asymptotic traffic flow in Gromov's hyperbolic graphs. We prove that under certain mild hypotheses the traffic flow in a hyperbolic graph tends to pass through a finite set of highly congested nodes. These nodes…

Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…

This paper proposes a simplified version of classical models for urban transportation networks, and studies the problem of controlling intersections with the goal of optimizing network-wide congestion. Differently from traditional…

We consider two elementary (max-flow and uniform-flow) and two realistic (max-min fairness and proportional fairness) congestion control schemes, and analyse how the algorithms and network structure affect throughput, the fairness of flow…

The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly…

The conventional view of the congestion control problem in data networks is based on the principle that a flow's performance is uniquely determined by the state of its bottleneck link, regardless of the topological properties of the…

Let a random geometric graph be defined in the supercritical regime for the existence of a unique infinite connected component in Euclidean space. Consider the first-passage percolation model with independent and identically distributed…

Large real-world networks are typically scale-free. Recent research has shown that such graphs are described best in a geometric space. More precisely, the internet can be mapped to a hyperbolic space such that geometric greedy routing…

Internet is known to display a highly heterogeneous structure and complex fluctuations in its traffic dynamics. Congestion seems to be an inevitable result of user's behavior coupled to the network dynamics and it effects should be…