A method based on k-shell decomposition to identify influential nodes in complex networks

Journal of Statistical Mechanics: Theory and Experiment, 2008(10), P10008

Polycyclic aromatic compounds (PACs) are known due to their mutagenic activity. Among them, 2-nitrobenzanthrone (2-NBA) and 3-nitrobenzanthrone (3-NBA) are considered as two of the most potent mutagens found in atmospheric particles. In the present study 2-NBA, 3-NBA and selected PAHs and Nitro-PAHs were determined in fine particle samples (PM 2.5) collected in a bus station and an outdoor site. The fuel used by buses was a diesel-biodiesel (96:4) blend and light-duty vehicles run with any ethanol-to-gasoline proportion. The concentrations of 2-NBA and 3-NBA were, on average, under 14.8 µg g−1 and 4.39 µg g−1, respectively. In order to access the main sources and formation routes of these compounds, we performed ternary correlations and multivariate statistical analyses. The main sources for the studied compounds in the bus station were diesel/biodiesel exhaust followed by floor resuspension. In the coastal site, vehicular emission, photochemical formation and wood combustion were the main sources for 2-NBA and 3-NBA as well as the other PACs. Incremental lifetime cancer risk (ILCR) were calculated for both places, which presented low values, showing low cancer risk incidence although the ILCR values for the bus station were around 2.5 times higher than the ILCR from the coastal site.

Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as "modularity" over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times. I illustrate the method with applications to several published network data sets.