Let G be a simple n-vertex graph whose eigenvalues are λ1, . . . , λn. The Estrada index of G is defined as EE(G) = ∑n i=1 e λi . The importance of this topological index extends much further than just pure graph theory. For example, it has been used to quantify the degree of folding of proteins and to measure centrality of complex networks. The talk aims to give an introduction to the Estrada ...

As an example of “big data,” we consider a repository of Arctic sea ice concentration data collected from satellites over the years 1979-2005. The data is represented by a graph, where vertices correspond to measurement points, and an edge is inserted between two vertices if the Pearson correlation coefficient between them exceeds a threshold. We investigate new questions about the structure of...

We consider the all pairs all shortest paths (APASP) problem, which maintains the shortest path dag rooted at every vertex in a directed graph G = (V,E) with positive edge weights. For this problem we present a decremental algorithm (that supports the deletion of a vertex, or weight increases on edges incident to a vertex). Our algorithm runs in amortized O(ν · log n) time per update, where n =...

This paper proposes a novel generalisation model for selecting characteristic streets in an urban street network. This model retains the central structure of a street network. It relies on a structural representation of a street network using graph principles where vertices represent named streets and links represent street intersections. Based on this representation, so-called connectivity gra...

There exist graphs of which all detours are Hamiltonian paths. Such graphs are called by Diudea (J. Chem. Inf. Comput. Sci. 1997, 37, 1101-1108) full Hamiltonian detour FHΔ graphs. These graphs show the maximal value of the Detour index while the minimal value of the Cluj-Detour index. A selected set of cubic graphs on 16 vertices is tested for the distribution of the relative centrality RC val...

The robustness of networks is an important problem that has been studied in a variety of situations, see for instance [3] or the survey [5] and the references therein. A milestone in the study of this problem was the discovery by Albert et al. of the dramatic effect of targeted attacks on networks whose vertex degrees follow a power-law distribution, like the Internet and the World Wide Web [1]...

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A novel algorithm for the fast detection of hubs in chemical networks is presented. The algorithm identifies a set of nodes in the network as most significant, aimed to be the most effective points of distribution for fast, widespread coverage throughout the system. We show that our hubs have in general greater closeness centrality and betweenness centrality than vertices with maximal degree, w...

During the upcoming Run 3 and 4 at LHC upgraded ALICE (A Large Ion Collider Experiment) will operate a significantly higher luminosity collect two orders of magnitude more events than in 1 2. A part upgrade is new Fast Interaction Trigger (FIT). This thoroughly redesigned detector combines, one system, functionality four forward detectors used by during 2: T0, V0, FMD, AD. The FIT monitor backg...