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This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…
Traditional measures of closeness and betweenness centrality in networks rely on the shortest paths between nodes. Many standard metrics fail to accurately reflect the physical or probabilistic characteristics of nodal centrality and…
Proximity measures on graphs have a variety of applications in network analysis, including community detection. Previously they have been mainly studied in the context of networks without attributes. If node attributes are taken into…
Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to…
An ordinal-valued metric taking its values in the set of all countable ordinals can be assigned to a metrizable set of nodes in a transfinite graph. Then, a variety of results concerning nodal eccentricities, radii, diameters, centers,…
Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be…
Centrality is an important notion in complex networks; it could be used to characterize how influential a node or an edge is in the network. It plays an important role in several other network analysis tools including community detection.…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
This paper presents a formal definition of stability for node centrality measures in weighted graphs. It is shown that the commonly used measures of degree, closeness and eigenvector centrality are stable whereas betweenness centrality is…
The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central…
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…
Centrality measures for simple graphs/networks are well-defined and each has numerous main-memory algorithms. However, for modeling complex data sets with multiple types of entities and relationships, simple graphs are not ideal. Multilayer…
Centrality metrics are a popular tool in Network Science to identify important nodes within a graph. We introduce the Potential Gain as a centrality measure that unifies many walk-based centrality metrics in graphs and captures the notion…
In this thesis I propose an algorithm to heuristically calculate different distance measures on uncertain graphs (i.e. graphs where edges only exist with a certain probability) and apply this to the heuristic calculation of harmonic…
Mapper graphs are widely used tools in topological data analysis and visualization. They can be understood as discrete approximations of Reeb graphs, providing insight into the shape and connectivity of complex data. Given a…
We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let $\Gamma$ be a graph with vertex set $V$, diameter $D$, adjacency matrix $A$, and…
We consider the normalized Laplace operator for directed graphs with positive and negative edge weights. This generalization of the normalized Laplace operator for undirected graphs is used to characterize directed acyclic graphs. Moreover,…
Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were…
Centrality is a key property of complex networks that influences the behavior of dynamical processes, like synchronization and epidemic spreading, and can bring important information about the organization of complex systems, like our brain…
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…