Collective synchronization induced by epidemic dynamics on complex networks with communities

Much recent empirical evidence shows that \textit{community structure} is ubiquitous in the real-world networks. In this Letter, we propose a growth model to create scale-free networks with the tunable strength (noted by $Q$) of community structure and investigate the influence of community strength upon the collective synchronization induced by SIRS epidemiological process. Global and local synchronizability of the system is studied by means of an order parameter and the relevant finite-size scaling analysis is provided. The numerical results show that, a phase transition occurs at $Q_c\simeq0.835$ from global synchronization to desynchronization and the local synchronization is weakened in a range of intermediately large $Q$. Moreover, we study the impact of mean degree $$ upon synchronization on scale-free networks.Comment: 5 pages, 4 figures. to appeared in Phys. Rev. E 75 (2007

Tris(1,10-phenanthroline-κ2 N,N′)nickel(II) bis­(2,4,5-tricarb­oxy­benzo­ate) monohydrate

In the title compound, [Ni(C12H8N2)3](C10H5O8)2·H2O, the NiII cation is coordinated by six N atoms of the three bidentate chelating 1,10-phenanthroline ligands in a slightly distorted octa­hedral coordination geometry. The Ni—N bond lengths range from 2.074 (2) to 2.094 (2) Å. The dihedral angles between the three chelating NCCN groups to each other are 85.71 (3), 73.75 (2) and 85.71 (3)°, respectively. The Ni cation, the phenyl ring of the 1,10-phenanthroline ligand and the lattice water molecule are located on special positions (site symmetry 2). In the crystal, the uncoordinated 2,4,5-tricarb­oxy­benzeno­ate anions join with each other through O—H⋯O hydrogen bonds, forming a two-dimensional hydrogen-bonded layer structure along the bc plane. The layers are further linked via additional O—H⋯O inter­actions between water and carboxyl groups, resulting in a three-dimensional supra­molecular network

Link prediction in evolving networks based on popularity of nodes

Link prediction aims to uncover the underlying relationship behind networks, which could be utilized to predict missing edges or identify the spurious edges. The key issue of link prediction is to estimate the likelihood of potential links in networks. Most classical static-structure based methods ignore the temporal aspects of networks, limited by the time-varying features, such approaches perform poorly in evolving networks. In this paper, we propose a hypothesis that the ability of each node to attract links depends not only on its structural importance, but also on its current popularity (activeness), since active nodes have much more probability to attract future links. Then a novel approach named popularity based structural perturbation method (PBSPM) and its fast algorithm are proposed to characterize the likelihood of an edge from both existing connectivity structure and current popularity of its two endpoints. Experiments on six evolving networks show that the proposed methods outperform state-of-the-art methods in accuracy and robustness. Besides, visual results and statistical analysis reveal that the proposed methods are inclined to predict future edges between active nodes, rather than edges between inactive nodes