3-[(Cyclo­hexyl­idene)amino]-1-(4-methyl­phen­yl)thio­urea

In the title compound, C14H19N3S, the cyclo­hexane ring has a chair conformation. The almost planar amino­thio­urea unit (r.m.s. deviation = 0.0062 Å) is aligned at a dihedral angle of 45.23 (8)° with respect to the benzene ring. Inter­molecular N—H⋯N and N—H⋯S hydrogen bonding stabilizes the crystal structure

(E)-1-(4-Methyl­phen­yl)-3-[(1-phenyl­ethyl­idene)amino]­thio­urea

In the title compound, C16H17N3S, the amino­thio­urea unit is nearly planar (r.m.s. deviation = 0.0425 Å), and is twisted with respect to the tolyl and phenyl rings by 57.84 (7) and 15.88 (14)°, respectively; the tolyl and phenyl rings are twisted by 65.64 (11)° to each other. Inter­molecular N—H⋯S and weak C—H⋯S hydrogen bonds are present in the crystal structure

Ethyl 3-[2-(p-tolyl­carbamothio­yl)hydrazinyl­idene]butano­ate

The title compound, C14H19N3O2S, was obtained from a condensation reaction of N-(p-tol­yl)hydrazinecarbothio­amide and ethyl acetoacetate. The mol­ecule assumes an E configuration; the thio­semicarbazide and ester groups are located on the opposite sides of the C=N bond. The almost planar thio­semicarbazide unit (r.m.s. deviation = 0.0130 Å) is tilted at a dihedral angle of 49.54 (12)° with respect to the benzene ring. Inter­molecular N—H⋯N and N—H⋯S hydrogen bonding stabilizes the crystal structure. The eth­oxy group of the ester unit is disordered over two positions, with a site-occupancy ratio of 0.680 (10):0.320 (10)

3-[(Furan-2-yl­methyl­idene)amino]-1-(4-methyl­phen­yl)thio­urea

There are two independent mol­ecules in the asymmetric unit of the title compound, C13H13N3OS, which was obtained from a condensation reaction of N-(p-tol­yl)hydrazinecarbothio­amide and furfural. The dihedral angles between the mean planes of the tolyl ring and the (furan-2-yl­methyl­ene)hydrazine unit are 39.83 (8) and 48.95 (7)° in the two mol­ecules. The mol­ecules both exhibit an E configuration. In the crystal, inter­molecular N—H⋯N and N—H⋯S hydrogen bonds connect the two independent mol­ecules

1-Benzyl­idene­amino-3-(4-methyl­phen­yl)thio­urea

In the title compound, C15H15N3S, the almost planar 2-benzyl­idenehydrazinecarbothio­amide unit (r.m.s. deviation = 0.0351 Å) is aligned at a dihedral angle of 64.42 (6)° with respect to the plane of the tolyl ring. The mol­ecule exhibits an E configuration for the azomethine linkage. In the crystal, inter­molecular N—H⋯S hydrogen bonds about centers of inversion lead to the formation of dimers

5-(Pyridin-4-yl)isophthalic acid

In the title compound, C13H9NO4, the two carb­oxy­lic groups and the benzene ring are approximately co-planar with a maximum atomic deviation 0.175 (4) Å, while the pyridine ring is oriented at a dihedral angle of 31.07 (18)° with respect to the benzene ring. In the crystal, mol­ecules are linked by O—H⋯O, O—H⋯N and weak C—H⋯O hydrogen bonds, forming a three-dimensional supra­molecular framework

A dynamical approach to identify vertices centrality in complex networks

In this paper, we proposed a dynamical approach to assess vertices centrality according to the synchronization process of the Kuramoto model. In our approach, the vertices dynamical centrality is calculated based on the Difference of vertices Synchronization Abilities (DSA), which are different from traditional centrality measurements that are related to the topological properties. Through applying our approach to complex networks with a clear community structure, we have calculated all vertices' dynamical centrality and found that vertices at the end of weak links have higher dynamical centrality. Meanwhile, we analyzed the robustness and efficiency of our dynamical approach through testing the probabilities that some known vital vertices were recognized. Finally, we applied our dynamical approach to identify community due to its satisfactory performance in assessing overlapping vertices. Our present work provides a new perspective and tools to understand the crucial role of heterogeneity in revealing the interplay between the dynamics and structure of complex networks