Related papers: Network connectivity under a probabilistic node fa…
Cascading failures are the typical reasons of black- outs in power grids. The grid topology plays an important role in determining the dynamics of cascading failures in power grids. Measures for vulnerability analysis are crucial to assure…
Many community detection algorithms require the introduction of a measure on the set of nodes. Previously, a lot of efforts have been made to find the top-performing measures. In most cases, experiments were conducted on several datasets or…
Can we employ one neural model to efficiently dismantle many complex yet unique networks? This article provides an affirmative answer. Diverse real-world systems can be abstracted as complex networks each consisting of many functional nodes…
We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and…
To measure node importance, network scientists employ centrality scores that typically take a microscopic or macroscopic perspective, relying on node features or global network structure. However, traditional centrality measures such as…
Betweenness centrality (BC) is one of the most used centrality measures for network analysis, which seeks to describe the importance of nodes in a network in terms of the fraction of shortest paths that pass through them. It is key to many…
Several expressions for the $j$-th component $\left( x_{k}\right)_{j}$ of the $k$-th eigenvector $x_{k}$ of a symmetric matrix $A$ belonging to eigenvalue $\lambda_{k}$ and normalized as $x_{k}^{T}x_{k}=1$ are presented. In particular, the…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
In this article, we revisit and expand our prior work on graph similarity. As with our earlier work, we focus on a view of similarity which does not require node correspondence between graphs under comparison. Our work is suited to the…
Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e. the question of how good an algorithm…
Navigability is a distinctive features of graphs associated with artificial or natural systems whose primary goal is the transportation of information or goods. We say that a graph $\mathcal{G}$ is navigable when an agent is able to…
Who is more important in a network? Who controls the flow between the nodes or whose contribution is significant for connections? Centrality metrics play an important role while answering these questions. The betweenness metric is useful…
Centrality indices are used to rank the nodes of a graph by importance: this is a common need in many concrete situations (social networks, citation networks, web graphs, for instance) and it was discussed many times in sociology,…
Connectivity and controllability of a complex network are two important issues that guarantee a networked system to function. Robustness of connectivity and controllability guarantees the system to function properly and stably under various…
Centrality describes the importance of nodes in a graph and is modeled by various measures. Its global analogue, called centralization, is a general formula for calculating a graph-level centrality score based on the node-level centrality…
Centrality measures have been defined to quantify the importance of a node in complex networks. The relative importance of a node can be measured using its centrality rank based on the centrality value. In the present work, we predict the…
Network dismantling is to identify a minimal set of nodes whose removal breaks the network into small components of subextensive size. Because finding the optimal set of nodes is an NP-hard problem, several heuristic algorithms have been…
Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational…
Closeness Centrality (CC) and Betweenness Centrality (BC) are crucial metrics in network analysis, providing essential reference for discerning the significance of nodes within complex networks. These measures find wide applications in…
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…