Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks

We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality $C$ of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of both fractal and non-fractal scale-free networks have power law betweenness centrality distribution $P(C)\sim C^{-\delta}$. We find that for non-fractal scale-free networks $\delta = 2$, and for fractal scale-free networks $\delta = 2-1/d_{B}$, where $d_{B}$ is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network at AS level (N=20566), where $N$ is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to non-fractal networks upon adding random edges to a fractal network. We show that the crossover length $\ell^{*}$, separating fractal and non-fractal regimes, scales with dimension $d_{B}$ of the network as $p^{-1/d_{B}}$, where $p$ is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with $p$.Comment: 19 pages, 6 figures. Submitted to PR

Computing Vertex Centrality Measures in Massive Real Networks with a Neural Learning Model

Vertex centrality measures are a multi-purpose analysis tool, commonly used in many application environments to retrieve information and unveil knowledge from the graphs and network structural properties. However, the algorithms of such metrics are expensive in terms of computational resources when running real-time applications or massive real world networks. Thus, approximation techniques have been developed and used to compute the measures in such scenarios. In this paper, we demonstrate and analyze the use of neural network learning algorithms to tackle such task and compare their performance in terms of solution quality and computation time with other techniques from the literature. Our work offers several contributions. We highlight both the pros and cons of approximating centralities though neural learning. By empirical means and statistics, we then show that the regression model generated with a feedforward neural networks trained by the Levenberg-Marquardt algorithm is not only the best option considering computational resources, but also achieves the best solution quality for relevant applications and large-scale networks. Keywords: Vertex Centrality Measures, Neural Networks, Complex Network Models, Machine Learning, Regression ModelComment: 8 pages, 5 tables, 2 figures, version accepted at IJCNN 2018. arXiv admin note: text overlap with arXiv:1810.1176

Topology and energy transport in networks of interacting photosynthetic complexes

We address the role of topology in the energy transport process that occurs in networks of photosynthetic complexes. We take inspiration from light harvesting networks present in purple bacteria and simulate an incoherent dissipative energy transport process on more general and abstract networks, considering both regular structures (Cayley trees and hyperbranched fractals) and randomly-generated ones. We focus on the the two primary light harvesting complexes of purple bacteria, i.e., the LH1 and LH2, and we use network-theoretical centrality measures in order to select different LH1 arrangements. We show that different choices cause significant differences in the transport efficiencies, and that for regular networks centrality measures allow to identify arrangements that ensure transport efficiencies which are better than those obtained with a random disposition of the complexes. The optimal arrangements strongly depend on the dissipative nature of the dynamics and on the topological properties of the networks considered, and depending on the latter they are achieved by using global vs. local centrality measures. For randomly-generated networks a random arrangement of the complexes already provides efficient transport, and this suggests the process is strong with respect to limited amount of control in the structure design and to the disorder inherent in the construction of randomly-assembled structures. Finally, we compare the networks considered with the real biological networks and find that the latter have in general better performances, due to their higher connectivity, but the former with optimal arrangements can mimic the real networks' behaviour for a specific range of transport parameters. These results show that the use of network-theoretical concepts can be crucial for the characterization and design of efficient artificial energy transport networks.Comment: 14 pages, 16 figures, revised versio