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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely average path length, degree distribution and clustering coefficient. Although the…

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure…

The stability of a complex system generally decreases with increasing system size and interconnectivity, a counterintuitive result of widespread importance across the physical, life, and social sciences. Despite recent interest in the…

Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications agents may belong to different…

Laws of large numbers, starting from certain nonequilibrium measures, have been shown for the integrated current across a bond, and a tagged particle in one-dimensional symmetric nearest-neighbor simple exclusion [Ann. Inst. Henri Poincare…

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…

Reputation-based cooperation on social networks offers a causal mechanism between graph properties and social trust. Recent papers on the `structural microfoundations` of the society used this insight to show how demographic processes, such…

Networks of companies can be constructed by using return correlations. A crucial issue in this approach is to select the relevant correlations from the correlation matrix. In order to study this problem, we start from an empty graph with no…

The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…

Convergence of resource allocation algorithms is well covered in the literature as convergence to a steady state is important due to stability and performance. However, research is lacking when it comes to the propagation of change that…

Credit default risk arises from complex interactions among borrowers, financial institutions, and transaction-level behaviors. While strong tabular models remain highly competitive in credit scoring, they may fail to explicitly capture…

A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. A dominating set is connected if the subgraph induced by its vertices is connected. The connected domatic partition problem asks for…

The stability of the financial system is associated with systemic risk factors such as the concurrent default of numerous small obligors. Hence it is of utmost importance to study the mutual dependence of losses for different creditors in…

A social network is often divided into many factions. People are friends within each faction, while they are enemies of the other factions, and even my enemy's enemy is not necessarily my friend. This configuration can be described in terms…

Symmetries are widespread in physical, technological, biological, and social systems and networks, including power grids. The swing equation is a classic model for the dynamics of powergrid networks. The main goal of this paper is to…

We derive a composite centrality measure for general weighted and directed complex networks, based on measure standardisation and invariant statistical inheritance schemes. Different schemes generate different intermediate abstract measures…

The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all…

Adversarial robustness has received increasing attention along with the study of adversarial examples. So far, existing works show that robust models not only obtain robustness against various adversarial attacks but also boost the…

In this paper, we address a longstanding challenge in self-organized criticality (SOC) systems: establishing a connection between sandpiles and complex networks. Our approach employs a similarity-based transfer function characterized by two…