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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 employ the mathematical programming approach in conjunction with the graph theory to study the structure of correspondent banking networks. Optimizing the network requires decisions to be made to onboard, terminate or restrict the bank…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
Recently, the first author proposed a measure to calculate Pearson correlations for node values expressed in a network, by taking into account distances or metrics defined on the network. In this technical note, we show that using an…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent…
In this work we make an attempt to understand social networks from a mathematical viewpoint. In the first instance we consider a network where each node representing an individual can connect with a neighbouring node with a certain…
Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network $G$ of given length $L$ that is optimal in a certain sense. In the general model, the optimality…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to…
Inference and prediction of routes have become of interest over the past decade owing to a dramatic increase in package delivery and ride-sharing services. Given the underlying combinatorial structure and the incorporation of probabilities,…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
This work is divided into two main parts. The first part is devoted to exploring the connectivity of random subgraphs of cartesian products of $K_1$, $K_2$, and $P_3$. In the second part, the author presents a short review of the results…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…