Related papers: Spectral embedding for dynamic networks with stabi…

Graph embedding techniques are a staple of modern graph learning research. When using embeddings for downstream tasks such as classification, information about their stability and robustness, i.e., their susceptibility to sources of noise,…

Network representation learning in low dimensional vector space has attracted considerable attention in both academic and industrial domains. Most real-world networks are dynamic with addition/deletion of nodes and edges. The existing graph…

This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…

Real-world networks are composed of diverse interacting and evolving entities, while most of existing researches simply characterize them as particular static networks, without consideration of the evolution trend in dynamic networks.…

Network embedding assigns nodes in a network to low-dimensional representations and effectively preserves the network structure. Recently, a significant amount of progresses have been made toward this emerging network analysis paradigm. In…

In a dynamic network, the neighborhood of the vertices evolve across different temporal snapshots of the network. Accurate modeling of this temporal evolution can help solve complex tasks involving real-life social and interaction networks.…

The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…

A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…

The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…

Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. These representations can be used as features for a wide range of tasks on graphs such as classification, clustering, link prediction,…

We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…

This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…

Network embedding is a very important method for network data. However, most of the algorithms can only deal with static networks. In this paper, we propose an algorithm Recurrent Neural Network Embedding (RNNE) to deal with dynamic…

This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that…

Change detection in dynamic networks is an important problem in many areas, such as fraud detection, cyber intrusion detection and health care monitoring. It is a challenging problem because it involves a time sequence of graphs, each of…

The mixed membership stochastic blockmodel is a statistical model for a graph, which extends the stochastic blockmodel by allowing every node to randomly choose a different community each time a decision of whether to form an edge is made.…

One of the most common approaches to the analysis of dynamic networks is through time-window aggregation. The resulting representation is a sequence of static networks, i.e. the snapshot graph. Despite this representation being widely used…

As deep learning gains popularity in modelling dynamical systems, we expose an underappreciated misunderstanding relevant to modelling dynamics on networks. Strongly influenced by graph neural networks, latent vertex embeddings are…

The notions of noise sensitivity and stability were recently extended for the voter model. In this model, the vertices of a graph have opinions that are updated by uniformly selecting edges. We further extend stability results to different…

We systematically evaluate the (in-)stability of state-of-the-art node embedding algorithms due to randomness, i.e., the random variation of their outcomes given identical algorithms and graphs. We apply five node embeddings…