Related papers: Betweenness centrality in dense spatial networks
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in…
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,…
Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…
The problem of betweenness centrality remains a fundamental unsolved problem in complex networks. After a pioneering work by Barthelemy, it has been well-accepted that the maximal betweenness-degree ($b$-$k$) exponent for scale-free (SF)…
One of the more recent measures of centrality in social network analysis is the normalized harmonic centrality. A variant of the closeness centrality, harmonic centrality sums the inverse of the geodesic distances of each node to other…
Street network analysis holds appeal as a tool for the assessment of pedestrian connectivity and its relation to the intensity and mix of land-uses; however, application within urban-design triggers a range of questions on implementary…
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…
Complex networks have gained more attention from the last few years. The size of real-world complex networks, such as online social networks, WWW network, collaboration networks, is increasing exponentially with time. It is not feasible to…
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…
The calculation of centrality measures is common practice in the study of networks, as they attempt to quantify the importance of individual vertices, edges, or other components. Different centralities attempt to measure importance in…
In graph-based applications, a common task is to pinpoint the most important or ``central'' vertex in a (directed or undirected) graph, or rank the vertices of a graph according to their importance. To this end, a plethora of so-called…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
We study trade-offs presented by local search algorithms in complex networks which are heterogeneous in edge weights and node degree. We show that search based on a network measure, local betweenness centrality (LBC), utilizes the…
We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross…
Finding the important nodes in complex networks by topological structure is of great significance to network invulnerability. Several centrality measures have been proposed recently to evaluate the performance of nodes based on their…
Subgraph densities play a crucial role in network analysis, especially for the identification and interpretation of meaningful substructures in complex graphs. Localized subgraph densities, in particular, can provide valuable insights into…
The betweenness structure of a finite metric space $M = (X, d)$ is a pair $\mathcal{B}(M) = (X,\beta_M)$ where $\beta_M$ is the so-called betweenness relation of $M$ that consists of point triplets $(x, y, z)$ such that $d(x, z) = d(x, y) +…
Katz centrality (and its limiting case, eigenvector centrality) is a frequently used tool to measure the importance of a node in a network, and to rank the nodes accordingly. One reason for its popularity is that Katz centrality can be…
There is great significance in evaluating a node's Influence ranking in complex networks. Over the years, many researchers have presented different measures for quantifying node interconnectedness within networks. Therefore, this paper…