A novel self-adaptive SIS model based on the mutual interaction between a graph and its line graph.

We propose a new paradigm to design a network-based self-adaptive epidemic model that relies on the interplay between the network and its line graph. We implement this proposal on a susceptible-infected-susceptible model in which both nodes and edges are considered susceptible and their respective probabilities of being infected result in a real-time re-modulation of the weights of both the graph and its line graph. The new model can be considered as an appropriate perturbation of the standard susceptible-infected-susceptible model, and the coupling between the graph and its line graph is interpreted as a reinforcement factor that fosters diffusion through a continuous adjustment of the parameters involved. We study the existence and stability conditions of the endemic and disease-free states for general network topologies. Moreover, we introduce, through the asymptotic values in the endemic steady states, a new type of eigenvector centrality where the score of a node depends on both the neighboring nodes and the edges connected to it. We also investigate the properties of this new model on some specific synthetic graphs, such as cycle, regular, and star graphs. Finally, we perform a series of numerical simulations and prove their effectiveness in capturing some empirical evidence on behavioral adoption mechanisms.

Unraveling the key drivers of community composition in the agri-food trade network.

In the complex global food system, the dynamics associated with international food trade have become crucial determinants of food security. In this paper, we employ a community detection approach along with a supervised learning technique to explore the evolution of communities in the agri-food trade network and to identify key factors influencing their composition. By leveraging a large dataset that includes both volume and monetary value of trades, we identify similarities between countries and uncover the primary drivers that shape trade dynamics over time. The analysis also takes into account the impact of evolving climate conditions on food production and trading. The results highlight how the network's topological structure is continuously evolving, influencing the composition of communities over time. Alongside geographical proximity and geo-political relations, our analysis identifies sustainability, climate and food nutrition aspects as emerging factors that contribute to explaining trade relationships. These findings shed light on the intricate interactions within the global food trade system and provide valuable insights into the factors affecting its stability.

Smart network based portfolios.

In this article we deal with the problem of portfolio allocation by enhancing network theory tools. We propose the use of the correlation network dependence structure in constructing some well-known risk-based models in which the estimation of the correlation matrix is a building block in the portfolio optimization. We formulate and solve all these portfolio allocation problems using both the standard approach and the network-based approach. Moreover, in constructing the network-based portfolios we propose the use of three different estimators for the covariance matrix: the sample, the shrinkage toward constant correlation and the depth-based estimators . All the strategies under analysis are implemented on three high-dimensional portfolios having different characteristics. We find that the network-based portfolio consistently performs better and has lower risk compared to the corresponding standard portfolio in an out-of-sample perspective. Supplementary Information: The online version contains supplementary material available at 10.1007/s10479-022-04675-7.

Bounding the HL-index of a graph: a majorization approach.

In mathematical chemistry, the median eigenvalues of the adjacency matrix of a molecular graph are strictly related to orbital energies and molecular orbitals. In this regard, the difference between the occupied orbital of highest energy (HOMO) and the unoccupied orbital of lowest energy (LUMO) has been investigated (see Fowler and Pisansky in Acta Chim. Slov. 57:513-517, 2010). Motivated by the HOMO-LUMO separation problem, Jaklic et al. in (Ars Math. Contemp. 5:99-115, 2012) proposed the notion of HL-index that measures how large in absolute value are the median eigenvalues of the adjacency matrix. Several bounds for this index have been provided in the literature. The aim of the paper is to derive alternative inequalities to bound the HL-index. By applying majorization techniques and making use of some known relations, we derive new and sharper upper bounds for this index. Analytical and numerical results show the performance of these bounds on different classes of graphs.