The decrease of the spectral radius, an important characterizer of network dynamics, by removing links is investigated. The minimization of the spectral radius by removing m links is shown to be an NP-complete problem, which suggests considering heuristic strategies. Several greedy strategies are compared, and several bounds on the decrease of the spectral radius are derived. The strategy that removes that link l = i ∼ j with largest product (x 1 ) i (x 1 ) j of the components of the eigenvector x 1 belonging to the largest adjacency eigenvalue is shown to be superior to other strategies in most cases. Furthermore, a scaling law where the decrease in spectral radius is inversely proportional to the number of nodes N in the graph is deduced. Another sublinear scaling law of the decrease in spectral radius versus the number m of removed links is conjectured.

Abstract. An increasing number of network metrics have been applied in network analysis. If metric relations were known better, we could more effectively characterize networks by a small set of metrics to discover the association between network properties/metrics and network functioning. In this paper, we investigate the linear correlation coefficients between widely studied network metrics in three network models (Bárabasi-Albert graphs, Erdös-Rényi random graphs and Watts-Strogatz small-world graphs) as well as in functional brain networks of healthy subjects. The metric correlations, which we have observed and theoretically explained, motivate us to propose a small representative set of metrics by including only one metric from each subset of mutually strongly dependent metrics. The following contributions are considered important. The correlation of metrics in complex networks with applications in functional brain networks metrics so far, the average shortest path length and the clustering coefficient, are strongly correlated and, thus, redundant. Whereas spectral metrics, though only studied recently in the context of complex networks, seem to be essential in network characterizations. This representative set of metrics tends to both sufficiently and effectively characterize networks with a given degree distribution.In the study of a specific network, however, we have to at least consider the representative set so that important network properties will not be neglected.

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Two novel titanium alloys, Ti-10V-2Cr-3Al and Ti-10V-1Fe-3Al (wt%), have been designed, fabricated, and tested for their intended stress-induced martensitic (SIM) transformation behavior. The results show that for Ti-10V-1Fe-3Al the triggering stress for SIM transformation is independently affected by the b domain size and b phase stability, when the value of the molybdenum equivalent is higher than *9. The triggering stress was well predicted using the equations derived separately for the commercial Ti-10V-2Fe-3Al alloy. For samples containing b with a lower molybdenum equivalence value, pre-existing thermal martensite is also present and this was found to have an obstructive effect on SIM transformation. In Ti-10V-2Cr-3Al, the low diffusion speed of Cr caused local gradients in the Cr level for many heat treatments leading even to martensite free zones near former b regions.