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Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect…
In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
Inspired by a concept in comparative genomics, we investigate properties of randomly chosen members of G_1(m,n,t), the set of bipartite graphs with $m$ left vertices, n right vertices, t edges, and each vertex of degree at least one. We…
Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood and determined…
Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…
How can the `affinity' or `strength' of ties of a random graph be characterized and compactly represented? How can concepts like Fourier and inverse-Fourier like transform be developed for graph data? To do so, we introduce a new…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. Notably,…
We study a class of directed random graphs. In these graphs, the interval [0,x] is the vertex set, and from each y\in [0,x], directed links are drawn to points in the interval (y,x] which are chosen uniformly with density one. We analyze…
A rotor-router walk is a deterministic version of a random walk, in which the walker is routed to each of the neighbouring vertices in some fixed cyclic order. We consider here directed covers of graphs (called also periodic trees) and we…
We obtain sharp bounds for the number of n-cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be imagined. En route, we prove some sharp estimates on power…
This paper explores the conditions for determining fixed nodes in structured networks, specifically focusing on directed acyclic graphs (DAGs). We introduce several necessary and sufficient conditions for determining fixed nodes in…
In this paper, we study a hypothesis test to determine the underlying directed graph structure of nodes in a network, where the nodes represent random processes and the direction of the links indicate a causal relationship between said…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…