Related papers: Rapid Mixing of Local Graph Dynamics
Graph rewiring has emerged as a key technique to alleviate over-squashing in Graph Neural Networks (GNNs) and Graph Transformers by modifying the graph topology to improve information flow. While effective, rewiring inherently alters the…
The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…
Graph Neural Networks (GNNs) are popular models for machine learning on graphs that typically follow the message-passing paradigm, whereby the feature of a node is updated recursively upon aggregating information over its neighbors. While…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
Local thresholding algorithms were first presented more than a decade ago and have since been applied to a variety of data mining tasks in peer-to-peer systems, wireless sensor networks, and in grid systems. One critical assumption made by…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
Graph neural networks are experiencing a surge of popularity within the machine learning community due to their ability to adapt to non-Euclidean domains and instil inductive biases. Despite this, their stability, i.e., their robustness to…
We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us…
The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…
Many real world networks are characterized by adaptive changes in their topology depending on the dynamic state of their nodes. Here we study epidemic dynamics in an adaptive network, where susceptibles are able to avoid contact with…
Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…
In this paper, we present an algorithm for optimizing synchronizability of complex dynamical networks. Based on some network properties, rewirings, i.e. eliminating an edge and creating a new edge elsewhere, are performed iteratively…
The apparent disconnection between the microscopic and the macroscopic is a major issue in the understanding of complex systems. To this extend, we study the convergence of repeatedly applying local rules on a network, and touch on the…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
Dynamic graph learning equips the edges with time attributes and allows multiple links between two nodes, which is a crucial technology for understanding evolving data scenarios like traffic prediction and recommendation systems. Existing…
We investigate the emergence and persistence of communities through a recently proposed mechanism of adaptive rewiring in coevolutionary networks. We characterize the topological structures arising in a coevolutionary network subject to an…
In this contribution we introduce local attachment as an universal network-joining protocol for peer-to-peer networks, social networks, or other kinds of networks. Based on this protocol nodes in a finite-size network dynamically create…
The present paper studies local distributed graph problems in highly dynamic networks. Communication and changes of the graph happen in synchronous rounds and our algorithms always, i.e., in every round, satisfy non-trivial guarantees, no…
Networks created and maintained by social processes, such as the human friendship network and the World Wide Web, appear to exhibit the property of navigability: namely, not only do short paths exist between any pair of nodes, but such…