Related papers: Graph-theoretical Constructions for Graph Entropy …
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…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
The aim of this thesis is to investigate how the structure of a digraph affects its dichromatic number and to extend various results on undirected colouring to digraphs. In the first part of this thesis, we examine how the dichromatic…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder:…
We investigate how the underlying graph of a network supports a flow between a source node and a destination node and propose to compute the expected number of nodes and links that contribute to transferring items in random graphs. Since…
EDA problems are graph-structured, but not all graph-structured problems call for the same GNN computation. We argue that successful GNN-for-EDA methods are those whose propagation, aggregation, and supervision align with the native algebra…
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which…
We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors in previous papers. In particular, we prove the homotopy…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
As a result of the interaction of rapid development and competition in information technologies, the reliability of a network and how solid it remains is important. It is called the hat vulnerability of the network to measure the endurance…
A distinguishing coloring of a graph is a vertex coloring such that only the identity automorphism of the graph preserves the coloring. A 2-distinguishable graph is a graph which can be distinguished using 2 colors. The cost $\rho(G)$ of a…
Entanglement is a complexity measure of digraphs that origins in fixed-point logics. Its combinatorial purpose is to measure the nested depth of cycles in digraphs. We address the problem of characterizing the structure of graphs of…
The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and was introduced by J.…
This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…