Related papers: Algebraic connectivity of layered path graphs unde…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
The exploitation of graph structures is the key to effectively learning representations of nodes that preserve useful information in graphs. A remarkable property of graph is that a latent hierarchical grouping of nodes exists in a global…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
The network connectivity in a group of cooperative robots can be easily broken if one of them loses its connectivity with the rest of the group. In case of having robustness with respect to one-robot-fail, the communication network is…
Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which node-removal order has the greatest impact on the network structure? We approach this well-known problem for the first time…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
The edge-connectivity of a graph is the minimum number of edges whose deletion disconnects the graph. Let $\Delta(G)$ the maximum degree of a graph $G$ and let $\rho(G)$ be the spectral radius of $G$. In this article we present a lower…
Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…
The class of graph deletion problems has been extensively studied in theoretical computer science, particularly in the field of parameterized complexity. Recently, a new notion of graph deletion problems was introduced, called deletion to…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. In particular, we are interested in…
The problem of node-similarity in networks has motivated a plethora of such measures between node-pairs, which make use of the underlying graph structure. However, higher-order relations cannot be losslessly captured by mere graphs and…
Understanding the structure of a graph along with the structure of its subgraphs is important for several problems in graph theory. Two examples are the Reconstruction Conjecture and isomorph-free generation. This paper raises the question…
We investigate the bounds on algebraic connectivity of graphs subject to constraints on the number of edges, vertices, and topology. We show that the algebraic connectivity for any tree on $n$ vertices and with maximum degree $d$ is bounded…
Graphlets are subgraphs rooted at a fixed vertex. The number of occurrences of graphlets aligned to a particular vertex, called graphlet degree sequence (gds), gives a topological description of the surrounding of the analyzed vertex.…
We present a new, novel approach to obtaining a network's connectivity. More specifically, we show that there exists a relationship between a network's graph isoperimetric properties and its conditional connectivity. A network's…
Graphs and complex networks can be successively separated into connected components associated to respective seed nodes, therefore establishing a respective hierarchical organization. In the present work, we study the properties of the…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…