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Analysis of a network in terms of vulnerability is one of the most significant problems. Graph theory serves as a valuable tool for solving complex network problems, and there exist numerous graph-theoretic parameters to analyze the…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
The operability of a network concerns its ability to remain operational, despite possible failures in its links or equipment. One may model the network through a graph to evaluate and increase this operability. Its vertices and edges…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
This paper deals with three graph characteristics related to graph covering named the (vertex, edge, and total, resp.) H-irregularity strength of a graph G admitting H-covering. Those are the minimum values of positive integer k such that G…
In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…
The bondage number $b(G)$ of a graph $G$ is the cardinality of a minimum edge set whose removal from $G$ results in a graph with the domination number greater than that of $G$. It is a parameter to measure the vulnerability of a…
We derive attainable upper bounds on the algebraic connectivity (spectral gap) of a regular graph in terms of its diameter and girth. This bound agrees with the well-known Alon-Boppana-Friedman bound for graphs of even diameter, but is an…
The atom-bond sum-connectivity (ABS) index of a graph $G$ with edges $e_1,\cdots,e_m$ is the sum of the numbers $\sqrt{1-2(d_{e_i}+2)^{-1}}$ over $1\le i \le m$, where $d_{e_i}$ is the number of edges adjacent with $e_i$. In this paper, we…
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…
As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality…
This paper, we explore the dynamics of threshold networks on undirected signed graphs. Much attention has been dedicated to understanding the convergence and long-term behavior of this model. Yet, an open question persists: How does the…
Advanced Persistent Threats (APTs) are a main impendence in cyber security of computer networks. In 2015, a successful breach remains undetected 146 days on average, reported by [Fi16].With our work we demonstrate a feasible and fast way to…
Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale…
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank…
Subgraph densities play a crucial role in network analysis, especially for the identification and interpretation of meaningful substructures in complex graphs. Localized subgraph densities, in particular, can provide valuable insights into…
In this paper, we study crucial elements of a complex network, namely its nodes and connections, which play a key role in maintaining the network's structure and function under unexpected structural perturbations of nodes and edges removal.…
In distributed networks, it is often useful for the nodes to be aware of dense subgraphs, e.g., such a dense subgraph could reveal dense subtructures in otherwise sparse graphs (e.g. the World Wide Web or social networks); these might…
With increasingly ambitious initiatives such as GENI and FIND that seek to design the future Internet, it becomes imperative to define the characteristics of robust topologies, and build future networks optimized for robustness. This paper…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…