Related papers: Rapid Mixing of Local Graph Dynamics
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
In this paper, a new information theoretic framework for graph matching is introduced. Using this framework, the graph isomorphism and seeded graph matching problems are studied. The maximum degree algorithm for graph isomorphism is…
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…
In this paper, we study a model of opinion dynamics in a social network in the presence increasing interpersonal influence, i.e., increasing peer pressure. Each agent in the social network has a distinct social stress function given by a…
Distributed peer-to-peer systems are widely popular due to their decentralized nature, which ensures that no peer is critical for the functionality of the system. However, fully decentralized solutions are usually much harder to design, and…
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
Graph Neural Networks (GNNs) excel at analyzing graph-structured data but struggle on heterophilic graphs, where connected nodes often belong to different classes. While this challenge is commonly addressed with specialized GNN…
We prove that any Markov chain that performs local, reversible updates on randomly chosen vertices of a bounded-degree graph necessarily has mixing time at least $\Omega(n\log n)$, where $n$ is the number of vertices. Our bound applies to…
We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…
Addictive behavior spreads through social networks via feedback among choice, peer pressure, and shifting ties, a process that eludes standard epidemic models. We present a comprehensive multi-state network model that integrates…
Sufficient conditions of consensus (synchronization) in networks described by digraphs and consisting of identical determenistic SIMO systems are derived. Identical and nonidentical control gains (positive arc weights) are considered.…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
Graph augmentation is a fundamental and well-studied problem that arises in network optimization. We consider a new variant of this model motivated by reconfigurable communication networks. In this variant, we consider a given physical…
Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
Graphs are widespread data structures used to model a wide variety of problems. The sheer amount of data to be processed has prompted the creation of a myriad of systems that help us cope with massive scale graphs. The pressure to deliver…
Mesh-based simulation using Graph Neural Networks (GNNs) has been recognized as a promising approach for modeling fluid dynamics. However, the mesh refinement techniques which allocate finer resolution to regions with steep gradients can…
Researches on analyzing graphs with Graph Neural Networks (GNNs) have been receiving more and more attention because of the great expressive power of graphs. GNNs map the adjacency matrix and node features to node representations by message…