Related papers: Identifying vital nodes by Achlioptas process

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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…

Cascading failures represent a fundamental threat to the integrity of complex systems, often precipitating a comprehensive collapse across diverse infrastructures and financial networks. This research articulates a robust and pragmatic…

The application of machine learning in the study of phase transitions has achieved remarkable success in both equilibrium and non-equilibrium systems. It is widely recognized that unsupervised learning can retrieve phase transition…

In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a…

Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…

Many popular measures used in social network analysis, including centrality, are based on the random walk. The random walk is a model of a stochastic process where a node interacts with one other node at a time. However, the random walk may…

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…

Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In…

Percolation theory investigates systems of interconnected units, their resilience to damage and their propensity to propagation. For random networks we can solve the percolation problems analytically using the generating function formalism.…

Identifying the most influential nodes in information networks has been the focus of many research studies. This problem has crucial applications in various contexts, such as controlling the propagation of viruses or rumours in real-world…

Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…

Community detection is the task of identifying clusters or groups of nodes in a network where nodes within the same group are more connected with each other than with nodes in different groups. It has practical uses in identifying similar…

Social networks are discrete systems with a large amount of heterogeneity among nodes (individuals). Measures of centrality aim at a quantification of nodes' importance for structure and function. Here we ask to which extent the most…

Critical infrastructure networks are a key ingredient of modern society. We discuss a general method to spot the critical components of a critical infrastructure network, i.e. the nodes and the links fundamental to the perfect functioning…

Evaluating the importance of a network node is a crucial task in network science and graph data mining. H-index is a popular centrality measure for this task, however, there is still a lack of its interpretation from a rigorous statistical…

Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…

Identifying emerging influential or popular node/item in future on network is a current interest of the researchers. Most of previous works focus on identifying leaders in time evolving networks on the basis of network structure or node's…

Among the consequences of the disordered interaction topology underlying many social, techno- logical and biological systems, a particularly important one is that some nodes, just because of their position in the network, may have a…

In this work we investigate the problem of estimating the percolation centrality of every vertex in a graph. This centrality measure quantifies the importance of each vertex in a graph going through a contagious process. It is an open…