We investigate centrality properties and the existence of a finite confidence set for the rootnode in growing random tree models. We show that a continuous time branching processescalled the Crump-Mode-Jagers (CMJ) branching process is well-suited to analyze such randomtrees, and establish centrality and root inference properties of sublinear preferential attachmenttrees. We...

Graph Isomorphism is one of the classical problems of graph theory for which no deterministic polynomial-time algorithm is currently known, but has been neither proven to be NP-complete. Several heuristic algorithms have been proposed to determine whether or not two graphs are isomorphic (i.e., structurally the same). In this paper, we analyze the discriminating power of the well-known centrali...

Networks are commonly used to model traffic patterns, social interactions, or web pages. The vertices in a network do not possess the same characteristics: some vertices are naturally more connected and some vertices can be more important. Closeness centrality (CC) is a global metric that quantifies how important is a given vertex in the network. When the network is dynamic and keeps changing, ...

In the study of complex networks, vertex centrality measures are used to identify the most important vertices within a graph. A related problem is that of measuring the centrality of an edge. In this paper, we propose a novel edge centrality index rooted in quantum information. More specifically, we measure the importance of an edge in terms of the contribution that it gives to the Von Neumann ...

We propose a model of network growth aimed at mimicking the evolution of the World Wide Web. To this purpose, we take as a key quantity, in the network evolution, the centrality or importance of a vertex as measured by its PageRank. Using a preferential attachment rule and a rewiring procedure based on this quantity, we can reproduce most of the topological properties of

Centrality measures are used in network science to identify the most important vertices for transmission of information and dynamics on a graph. One these measures, introduced by Estrada collaborators, is $\beta$-subgraph centrality, which based exponential matrix $\beta A$, where $A$ adjacency graph $\beta$ real parameter ("inverse temperature"). We prove that algebraic $\beta$, two with equal...

Often an attacker tries to disconnect a network by destroying nodes or edges, while the defender counters using various resilience mechanisms. Examples include a music industry body attempting to close down a peer-to-peer file-sharing network; medics attempting to halt the spread of an infectious disease by selective vaccination; and a police agency trying to decapitate a terrorist organisation...

Often an attacker tries to disconnect a network by destroying nodes or edges, while the defender counters using various resilience mechanisms. Examples include a music industry body attempting to close down a peer-to-peer file-sharing network; medics attempting to halt the spread of an infectious disease by selective vaccination; and a police agency trying to decapitate a terrorist organisation...

Centrality describes the importance of nodes in a graph and is modeled by various measures. Its global analogue, called centralization, general formula for calculating graph-level centrality score based on node-level measure. The latter enables us to compare graphs extent which connections given network are concentrated single vertex or group vertices. One measures social analysis harmonic cent...

We now present a different type of connection between graphs and eigenvalues. In several applications, we wish to find influential vertices in a graph. For instance, suppose we model Twitter as a directed graph where there is an edge from user i to user j if i follows j. Then how can we measure importance of a user in the graph? One way of measuring it is look at the in-degree of a user, or the...