Related papers: Connectivity of random graphs after centrality-bas…
Link residual closeness is a newly proposed measure for network vulnerability. In this model, vertices are perfectly reliable and the links fail independently of each other. It measures the vulnerability even when the removal of links does…
Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
We investigate the problem of enforcing a desired centrality measure in complex networks, while still keeping the original pattern of the network. Specifically, by representing the network as a graph with suitable nodes and weighted edges,…
A very interesting matter of Network Science is assessing how complex a given network is. In other words, by how much does such a network departs from any general patterns which could be evoked for its description. Among other choices,…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
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…
This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of…
The problem of assigning centrality values to nodes and edges in graphs has been widely investigated during last years. Recently, a novel measure of node centrality has been proposed, called k-path centrality index, which is based on the…
Network metrics form a fundamental part of the network analysis toolbox. Used to quantitatively measure different aspects of the network, these metrics can give insights into the underlying network structure and function. In this work, we…
A central task in network analysis is to identify important nodes in a graph. Betweenness centrality (BC) is a popular centrality measure that captures the significance of nodes based on the number of shortest paths each node intersects…
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…
This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…
Networks created from real-world data contain some inaccuracies or noise, manifested as small changes in the network structure. An important question is whether these small changes can significantly affect the analysis results. In this…
Typing Yesterday into the search-bar of your browser provides a long list of websites with, in top places, a link to a video by The Beatles. The order your browser shows its search results is a notable example of the use of network…
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…
We study the size of connected components of random nearest-neighbor graphs with vertex set the points of a homogeneous Poisson point process in ${\mathbb{R}}^d$. The connectivity function is shown to decay superexponentially, and we…
In graph theory and network analysis, node degree is defined as a simple but powerful centrality to measure the local influence of node in a complex network. Preferential attachment based on node degree has been widely adopted for modeling…
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…
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…