Related papers: Scale-dependent measure of network centrality from…
In the study of small and large networks it is customary to perform a simple random walk, where the random walker jumps from one node to one of its neighbours with uniform probability. The properties of this random walk are intimately…
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…
Influential nodes play a critical role in boosting or curbing spreading phenomena in complex networks. Numerous centrality measures have been proposed for identifying and ranking the nodes according to their importance. Classical centrality…
When analyzing the statistical and topological characteristics of complex networks, an effective and convenient way is to compute the centralities for recognizing influential and significant nodes or structures, yet most of them are…
We consider diffusion on discrete measure spaces as encoded by Markovian semigroups arising from weighted graphs. We study whether the graph is uniquely determined if the diffusion is given up to order isomorphism. If the graph is recurrent…
Structure of real networked systems, such as social relationship, can be modeled as temporal networks in which each edge appears only at the prescribed time. Understanding the structure of temporal networks requires quantifying the…
The identification of the most influential spreaders in networks is important to control and understand the spreading capabilities of the system as well as to ensure an efficient information diffusion such as in rumor-like dynamics. Recent…
One of the most fundamental problems in large scale network analysis is to determine the importance of a particular node in a network. Betweenness centrality is the most widely used metric to measure the importance of a node in a network.…
The centrality in a network is often used to measure nodes' importance and model network effects on a certain outcome. Empirical studies widely adopt a two-stage procedure, which first estimates the centrality from the observed noisy…
Several centrality measures have been formulated to quantify the notion of 'importance' of actors in social networks. Current measures scrutinize either local or global connectivity of the nodes and have been found to be inadequate for…
Heterogeneity is a key aspect of complex networks, often emerging by looking at the distribution of node properties, from the milestone observations on the degree to the recent developments in mixing pattern estimation. Mixing patterns, in…
We construct and study a class of spectral graph wavelets by analogy with Hermitian wavelets on the real line. We provide a localization result that significantly improves upon those previously available, enabling application to highly…
Most network studies rely on an observed network that differs from the underlying network which is obfuscated by measurement errors. It is well known that such errors can have a severe impact on the reliability of network metrics,…
Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between…
Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social…
Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. Most prominent centrality measures can be expressed as an aggregation of influence flows between pairs of…
The challenges of graph stream algorithms are twofold. First, each edge needs to be processed only once, and second, it needs to work on highly constrained memory. Diffusion degree is a measure of node centrality that can be calculated (for…
We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…
Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…
Recently an increasing amount of research is devoted to the question of how the most influential nodes (seeds) can be found effectively in a complex network. There are a number of measures proposed for this purpose, for instance,…