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We introduce a self-organized model of graph evolution associated with preferential network random walkers. The idea is developed by using two different types of walkers, the interactions of which lead to a dynamic graph. The walkers of the…
The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as…
Augmentations are the key factor in determining the performance of any neural network as they provide a model with a critical edge in boosting its performance. Their ability to boost a model's robustness depends on two factors, viz-a-viz,…
We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time…
A graph is a very common and powerful data structure used for modeling communication and social networks. Models that generate graphs with arbitrary features are important basic technologies in repeated simulations of networks and…
Networks (graphs) in psychology are often restricted to settings without interventions. Here we consider a framework borrowed from biology that involves multiple interventions from different contexts (observations and experiments) in a…
Dynamic connectivity is a well-studied problem, but so far the most compelling progress has been confined to the edge-update model: maintain an understanding of connectivity in an undirected graph, subject to edge insertions and deletions.…
Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…
A stable population network is hard to interrupt without any ecological consequences. A communication blockage between patches may destabilize the populations in the ecological network. This work deals with the construction of a safe cut…
This work introduces NetDiff, an expressive graph denoising diffusion probabilistic architecture that generates wireless ad hoc network link topologies. Such networks, with directional antennas, can achieve unmatched performance when the…
Recently, transformer architectures for graphs emerged as an alternative to established techniques for machine learning with graphs, such as (message-passing) graph neural networks. So far, they have shown promising empirical results, e.g.,…
In this paper, we explore the reduction of functionality in a complex system as a consequence of cumulative random damage and imperfect reparation, a phenomenon modeled as a dynamical process on networks. We analyze the global…
We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…
Transformer has been popular in recent crowd counting work since it breaks the limited receptive field of traditional CNNs. However, since crowd images always contain a large number of similar patches, the self-attention mechanism in…
Graph-structured datasets usually have irregular graph sizes and connectivities, rendering the use of recent data augmentation techniques, such as Mixup, difficult. To tackle this challenge, we present the first Mixup-like graph…
Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…
We argue that Transformers are essentially graph-to-graph models, with sequences just being a special case. Attention weights are functionally equivalent to graph edges. Our Graph-to-Graph Transformer architecture makes this ability…
Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…