Related papers: Rapid Mixing of Local Graph Dynamics

Graph Neural Networks are powerful models for learning from graph-structured data, yet their effectiveness is often limited by two critical challenges: over-squashing, where information from distant nodes is excessively compressed, and…

The ability of a peer-to-peer (P2P) system to effectively host decentralized applications often relies on the availability of a peer-sampling service, which provides each participant with a random sample of other peers. Despite the…

The structure of the network has great impact on its traffic dynamics. Most of the real world networks follow the heterogeneous structure and exhibit scale-free feature. In scale-free network, a new node prefers to connect with hub nodes…

The Glauber dynamics on the colourings of a graph is a random process which consists in recolouring at each step a random vertex of a graph with a new colour chosen uniformly at random among the colours not already present in its…

When a link is occupied to restrict the growth of large clusters using the size information of a finite number of finite clusters, so-called local information, an abrupt but continuous transition is exhibited. We report here that a hybrid…

Graph neural networks have become a staple in problems addressing learning and analysis of data defined over graphs. However, several results suggest an inherent difficulty in extracting better performance by increasing the number of…

We study probabilistic protocols for concurrent threshold-based load balancing in networks. There are n resources or machines represented by nodes in an undirected graph and m >> n users that try to find an acceptable resource by moving…

We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie…

We consider a general model in which there is a coupled dynamics of node states and links states in a network. This coupled dynamics coevolves with dynamical changes of the topology of the network caused by a link rewiring mechanism. Such…

Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…

We consider the self organizing process of merging and regeneration of vertices in complex networks and demonstrate that a scale-free degree distribution emerges in a steady state of such a dynamics. The merging of neighbor vertices in a…

We study the problem of distributed consensus in networks where the local agents have high-order ($n\ge 3$) integrator dynamics, and where all feedback is localized in that each agent has a bounded number of neighbors. We prove that no…

We study convergence rates of random-order best-response dynamics in games on networks with linear best responses and strategic substitutes. Combining formal analysis with numerical simulations we identify phenomena that lead to slow…

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes…

We explore graph rewiring methods that optimise commute time. Recent graph rewiring approaches facilitate long-range interactions in sparse graphs, making such rewirings commute-time-optimal on average. However, when an expert prior exists…

We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of…

Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes…

This paper presents a self-organizing protocol for dynamic (unstructured P2P) overlay networks, which allows to react to the variability of node arrivals and departures. Through local interactions, the protocol avoids that the departure of…

We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a…

In a recent paper, Krapivsky and Redner (Phys. Rev. E, 71 (2005) 036118) proposed a new growing network model with new nodes being attached to a randomly selected node, as well to all ancestors of the target node. The model leads to a…