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. Newman's measure for (dis)assortativity, the linear degree correlation coefficient ρD, is reformulated in terms of the total number N k of walks in the graph with k hops. This reformulation allows us to derive a new formula from which a degree-preserving rewiring algorithm is deduced, that, in each rewiring step, either increases or decreases ρD conform our desired objective. Spectral metrics (eigenvalues of graph-related matrices), especially, the largest eigenvalue λ1 of the adjacency matrix and the algebraic connectivity μN−1 (second-smallest eigenvalue of the Laplacian) are powerful characterizers of dynamic processes on networks such as virus spreading and synchronization processes. We present various lower bounds for the largest eigenvalue λ1 of the adjacency matrix and we show, apart from some classes of graphs such as regular graphs or bipartite graphs, that the lower bounds for λ1 increase with ρD. A new upper bound for the algebraic connectivity μN−1 decreases with ρD. Applying the degree-preserving rewiring algorithm to various real-world networks illustrates that (a) assortative degree-preserving rewiring increases λ1, but decreases μN−1, even leading to disconnectivity of the networks in many disjoint clusters and that (b) disassortative degree-preserving rewiring decreases λ1, but increases the algebraic connectivity, at least in the initial rewirings.

The algebraic connectivity µ N −1 , i.e. the second smallest eigenvalue of the Laplacian matrix, plays a crucial role in dynamic phenomena such as diffusion processes, synchronization stability, and network robustness. In this work we study the algebraic connectivity in the general context of interdependent networks, or network-of-networks (NoN). The present work shows, both analytically and numerically, how the algebraic connectivity of NoNs experiences a transition. The transition is characterized by a saturation of the algebraic connectivity upon the addition of sufficient coupling links (between the two individual networks of a NoN). In practical terms, this shows that NoN topologies require only a fraction of coupling links in order to achieve optimal diffusivity. Furthermore, we observe a footprint of the transition on the properties of Fiedler's spectral bisection.

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.

Brain functioning such as cognitive performance depends on the functional interactions between brain areas, namely, the functional brain networks. The functional brain networks of a group of patients with brain tumors are measured before and after tumor resection. In this work, we perform a weighted network analysis to understand the effect of neurosurgery on the characteristics of functional brain networks. Statistically significant changes in network features have been discovered in the beta ͑13-30 Hz͒ band after neurosurgery: the link weight correlation around nodes and within triangles increases which implies improvement in local efficiency of information transfer and robustness; the clustering of high link weights in a subgraph becomes stronger, which enhances the global transport capability; and the decrease in the synchronization or virus spreading threshold, revealed by the increase in the largest eigenvalue of the adjacency matrix, which suggests again the improvement of information dissemination.

In recent years, transportation agencies and the general public alike are demanding increased considerations of sustainability in transport infrastructure. Warm mix asphalt (WMA) is developed for reducing energy consumptions and emissions in asphalt paving industry. In addition, the use of rubberized asphalt concrete (RAC) has proven to be economically and environmentally sound and effective in improving the performance of pavements around the world. The combination of WMA and RAC, namely WarmRAC, is a novel and promising paving technology that can realize pavement sustainability from principles to practices. This study summarizes the best practices and recent research findings on warm mix rubberized asphalt concrete, including mix design, construction techniques, performance evaluation, feasibility of recycling, and environmental and economic benefits. Although most research findings to date about WarmRAC are positive, it still has a long way for WarmRAC to be fully adopted worldwide. Therefore, life cycle assessment including environmental and economic impacts, and long-term performance of WarmRAC need further research with involvement of transportation agencies, industry and academia.

Expressions and bounds for Newman's modularity are presented. These results reveal conditions for or properties of the maximum modularity of a network. The influence of the spectrum of the modularity matrix on the maximum modularity is discussed. The second part of the paper investigates how the maximum modularity, the number of clusters, and the hop count of the shortest paths vary when the assortativity of the graph is changed via degree-preserving rewiring. Via simulations, we show that the maximum modularity increases, the number of clusters decreases, and the average hop count and the effective graph resistance increase with increasing assortativity.

Abstract. Newman's measure for (dis)assortativity, the linear degree correlation ρD, is widely studied although analytic insight into the assortativity of an arbitrary network remains far from well understood. In this paper, we derive the general relation (2), (3) (10) and (16) (6) and (15) of the assortativity. These results together with our numerical experiments in over 30 real-world complex networks illustrate that the assortativity range ρmax − ρmin is generally large in sparse networks, which underlines the importance of assortativity as a network characterizer.