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A number of recent works have concentrated on a few statistical properties of complex networks, such as the clustering, the right-skewed degree distribution and the community, which are common to many real world networks. In this paper, we…

The study of network robustness focuses on the way the overall functionality of a network is affected as some of its constituent parts fail. Failures can occur at random or be part of an intentional attack and, in general, networks behave…

Research on the robustness of the Internet has gained critical importance in the last decades because more and more individuals, societies and firms rely on this global network infrastructure for communication, knowledge transfer, business…

Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…

Damage scenarios for large networks are considered. The cascade scenario is described by means of powers of adjacency matrix. More difficult probabilistic variants of the large network damage are modeling by Markov chains. For reliability…

All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…

The purpose of this work is to test and study the hypothesis that residual networks are learning a perturbation from identity. Residual networks are enormously important deep learning models, with many theories attempting to explain how…

Many modern networks are \emph{reconfigurable}, in the sense that the topology of the network can be changed by the nodes in the network. For example, peer-to-peer, wireless and ad-hoc networks are reconfigurable. More generally, many…

The rapid expansion of global cloud infrastructures, coupled with the growing volume and complexity of network traffic, has fueled active research into scalable and resilient Traffic Engineering (TE) solutions for Wide Area Networks (WANs).…

Networks in nature rarely function in isolation but instead interact with one another with a form of a network of networks (NoN). A network of networks with interdependency between distinct networks contains instability of abrupt collapse…

In Nature, the primary goal of any network is to survive. This is less obvious for engineering networks (electric power, gas, water, transportation systems etc.) that are expected to operate under normal conditions most of time. As a…

Whether comparing networks to each other or to random expectation, measuring dissimilarity is essential to understanding the complex phenomena under study. However, determining the structural dissimilarity between networks is an ill-defined…

We study the question of reconstructing a weighted, directed network up to isomorphism from its motifs. In order to tackle this question we first relax the usual (strong) notion of graph isomorphism to obtain a relaxation that we call weak…

Tie strength prediction, sometimes named weight prediction, is vital in exploring the diversity of connectivity pattern emerged in networks. Due to the fundamental significance, it has drawn much attention in the field of network analysis…

Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological…

We analyze the performance of graph neural network (GNN) architectures from the perspective of random graph theory. Our approach promises to complement existing lenses on GNN analysis, such as combinatorial expressive power and worst-case…

Neural networks have demonstrated significant accuracy across various domains, yet their vulnerability to subtle input alterations remains a persistent challenge. Conventional methods like data augmentation, while effective to some extent,…

Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…

A tight alignment between the degree vector and the leading eigenvector arises naturally in networks with neutral degree mixing and the absence of local structures. Many real-world networks, however, violate both conditions. We derive…

Anomaly detection in massive networks has numerous theoretical and computational challenges, especially as the behavior to be detected becomes small in comparison to the larger network. This presentation focuses on recent results in three…