Related papers: Classical and quantum random-walk centrality measu…
Group centrality is an extension of the classical notion of centrality for individuals, to make it applicable to sets of them. We perform a SWOT (strengths, weaknesses, opportunities and threats) analysis of the use of group centrality in…
We present a comprehensive analysis of algebraic methods for controlling the stationary distribution of PageRank-like random walkers. Building upon existing literature, we compile and extend results regarding both structural control…
Here we present a range-limited approach to centrality measures in both non-weighted and weighted directed complex networks. We introduce an efficient method that generates for every node and every edge its betweenness centrality based on…
Many real world systems can be expressed as complex networks of interconnected nodes. It is frequently important to be able to quantify the relative importance of the various nodes in the network, a task accomplished by defining some…
Katz centrality is a popular network centrality measure. It takes a (weighted) count of all walks starting at each node, with an additional damping factor of $\alpha$ that tunes the influence of walks as lengths increase. We introduce a…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
Due to wide applications in diverse fields, random walks subject to stochastic resetting have attracted considerable attention in the last decade. In this paper, we study discrete-time random walks on complex network with multiple resetting…
We survey classical localization problems arising from quantum network models in symmetry class C and their mappings to history-dependent random walks on directed lattices. We describe how localization versus delocalization of trajectories…
In complex networks, centrality metrics quantify the connectivity of nodes and identify the most important ones in the transmission of signals. In many real world networks, especially in transportation systems, links are dynamic, i.e. their…
Centrality measures are used in network science to evaluate the centrality of vertices or the position they occupy in a network. There are a large number of centrality measures according to some criterion. However, the generalizations of…
Real-world networks typically exhibit several aspects, or layers, of interactions among their nodes. By permuting the role of the nodes and the layers, we establish a new criterion to construct the dual of a network. This approach allows to…
The analysis of multilayer networks is among the most active areas of network science, and there are now several methods to detect dense "communities" of nodes in multilayer networks. One way to define a community is as a set of nodes that…
Multi-layered network exploration (MuLaNE) problem is an important problem abstracted from many applications. In MuLaNE, there are multiple network layers where each node has an importance weight and each layer is explored by a random walk.…
In various applications involving complex networks, network measures are employed to assess the relative importance of network nodes. However, the robustness of such measures in the presence of link inaccuracies has not been well…
In real world complex networks, the importance of a node depends on two important parameters: 1. characteristics of the node, and 2. the context of the given application. The current literature contains several centrality measures that have…
Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to…
Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…
There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness…
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…
We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination…