Related papers: Laplacian Flows in Complex-valued Directed Network…
The aim of this paper is to discuss several aspects of connections between the p-Laplacian and mathematical models in hydrology. At first we present models of groundwater flow in phreatic aquifers and models of irrigation and drainage that…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
Identifying influential nodes and edges in directed networks remains a fundamental challenge across domains from social influence to biological regulation. Most existing centrality measures face a critical limitation: they either discard…
In this article we propose a generalization of two known invariants of real networks: degree and ksi-centrality. More precisely, we found a series of centralities based on Laplacian matrix, that have exponential distributions (power-law for…
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…
In this paper, we examine the controllability of Laplacian dynamic networks on cographs. Cographs appear in modeling a wide range of networks and include as special instances, the threshold graphs. In this work, we present necessary and…
Consensus on nonlinear spaces is of use in many control applications. This paper proposes a gradient descent flow algorithm for consensus on hypersurfaces. We show that if an inequality holds, then the system converges for almost all…
In this note, we examine the problem of identifying the interaction geometry among a known number of agents, adopting a consensus-type algorithm for their coordination. The proposed identification process is facilitated by introducing…
In this study, we analyzed the problem of accelerating the linear average consensus algorithm for complex networks. We propose a data-driven approach to tuning the weights of temporal (i.e., time-varying) networks using deep learning…
In manifold learning, algorithms based on graph Laplacians constructed from data have received considerable attention both in practical applications and theoretical analysis. In particular, the convergence of graph Laplacians obtained from…
Since the publication of 'Complex Contagions and the Weakness of Long Ties' in 2007, complex contagions have been studied across an enormous variety of social domains. In reviewing this decade of research, we discuss recent advancements in…
Finding semantic correspondences is a challenging problem. With the breakthrough of CNNs stronger features are available for tasks like classification but not specifically for the requirements of semantic matching. In the following we…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
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…
In this paper, we derive cumulant bounds for subgraph counts and power-weighted edge length in a class of spatial random networks known as weighted random connection models. This involves dealing with long-range spatial correlations induced…
Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such…
In this work, we consider a group of n agents whose interactions can be represented using unsigned or signed structurally balanced graphs or a special case of structurally unbalanced graphs. A Laplacian-based model is proposed to govern the…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
We study networks with linear dynamics where the presence of symmetries of the pair (A,B) induces a partition of the network nodes in clusters and the matrix A is not restricted to be in Laplacian form. For these networks, an invariant…