Diffusion on Complex Networks : A way to probe their large scale topological structures

A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to real-world networks like a friendship network of known modular structure, and an Internet routing network. For the friendship network, its known structure is well reproduced. In case of the Internet, where the structure is far less well-known, one indeed finds a modular structure, and modules can roughly be associated with individual countries. Quantitatively the modular structure of the Internet manifests itself in an approximately 10 times larger participation ratio of its slowest decaying modes as compared to the null model -- a random scale-free network. The extreme edges of the Internet are found to correspond to Russian and US military sites.Comment: Latex, 13 pages, 4 figures (To appear Physica A

The Architecture of a Novel Weighted Network: Knowledge Network

Networked structure emerged from a wide range of fields such as biological systems, World Wide Web and technological infrastructure. A deeply insight into the topological complexity of these networks has been gained. Some works start to pay attention to the weighted network, like the world-wide airport network and the collaboration network, where links are not binary, but have intensities. Here, we construct a novel knowledge network, through which we take the first step to uncover the topological structure of the knowledge system. Furthermore, the network is extended to the weighted one by assigning weights to the edges. Thus, we also investigate the relationship between the intensity of edges and the topological structure. These results provide a novel description to understand the hierarchies and organizational principles in knowledge system, and the interaction between the intensity of edges and topological structure. This system also provides a good paradigm to study weighted networks.Comment: 5 figures 11 page

Topological Defects and the Formation of Structure in the Universe

Topological defects, in particular cosmic strings, give rise to an interesting mechanism for generating the primordial perturbations in the early Universe which are required to explain the present structure. An overview of the cosmic string model will be given, focusing on the predictions of the theory for the large-scale structure of the Universe and for cosmic microwave background anisotropies.Comment: 12 pages, 4 figures, uses LATEX and eps

The structure of Inter-Urban traffic: A weighted network analysis

We study the structure of the network representing the interurban commuting traffic of the Sardinia region, Italy, which amounts to 375 municipalities and 1,600,000 inhabitants. We use a weighted network representation where vertices correspond to towns and the edges to the actual commuting flows among those. We characterize quantitatively both the topological and weighted properties of the resulting network. Interestingly, the statistical properties of commuting traffic exhibit complex features and non-trivial relations with the underlying topology. We characterize quantitatively the traffic backbone among large cities and we give evidences for a very high heterogeneity of the commuter flows around large cities. We also discuss the interplay between the topological and dynamical properties of the network as well as their relation with socio-demographic variables such as population and monthly income. This analysis may be useful at various stages in environmental planning and provides analytical tools for a wide spectrum of applications ranging from impact evaluation to decision-making and planning support.Comment: 12 pages, 12 figures, 4 tables; 1 missing ref added and minor revision

On-surface Assembly of Au-Dicyanoanthracene Coordination Structures on Au(111)

On-surface metal-organic coordination provides a promising way for synthesizing different two-dimensional lattice structures that have been predicted to possess exotic electronic properties. Using scanning tunneling microscopy (STM) and spectroscopy (STS), we studied the supramolecular self-assembly of 9,10-dicyanoanthracene (DCA) molecules on the Au(111) surface. Close-packed islands of DCA molecules and Au-DCA metal-organic coordination structures coexist on the Au(111) surface. Ordered DCA$_{3}$Au$_{2}$ metal-organic networks have a structure combining a honeycomb lattice of Au atoms with a kagome lattice of DCA molecules. Low-temperature STS experiments demonstrate the presence of a delocalized electronic state containing contributions from both the gold atom states and the lowest unoccupied molecular orbital of the DCA molecules. These findings are important for the future search of topological phases in metal-organic networks combining honeycomb and kagome lattices with strong spin-orbit coupling in heavy metal atoms

The Revival of Cosmic Strings

Cosmic strings are one-dimensional topological defects which could have been formed in the early stages of our Universe. They triggered a lot of interest, mainly for their cosmological implications: they could offer an alternative to inflation for the generation of density perturbations. It was shown however that cosmic strings lead to inconsistencies with the measurements of the cosmic microwave background temperature anisotropies. The picture is changed recently. It was shown that, on the one hand, cosmic strings can be generically formed in the framework of supersymmetric grand unified theories and that, on the other hand, cosmic superstrings could play the r\^ole of cosmic strings. There is also some possible observational support. All this lead to a revival of cosmic strings research and this is the topic of my lecture.Comment: 13 pages, Invited Lecture in " Pomeranian Workshop in Fundamental Cosmology" (Poland 2005), to be published in Annalen der Physi

Synchronization processes in complex networks

We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to well defined communities of nodes appear in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology and spectral graph analysis.Comment: 16 pages, 4 figures. To appear in Physica D "Special Issue on dynamics on complex networks

Topological kink states at a tilt boundary in gated multi-layer graphene

The search for new realization of topologically protected edge states is an active area of research. We show that a tilt boundary in gated multi-layer graphene supports topologically protected gapless kink states, associated with quantum valley Hall insulator (QVH). We investigate such kink states from two perspectives: the microscopic perspective of a tight-binding model and an ab-initio calculation on bilayer, and the perspective of symmetry protected topological (SPT) states for general multi-layer. We show that a AB-BA bilayer tilt boundary supports gapless kink states that are undeterred by strain concentrated at the boundary. Further, we establish the kink states as concrete examples of edge states of {\it time-reversal symmetric} ${\mathbb Z}$-type SPT, protected by no valley mixing, electron number conservation, and time reversal $T$ symmetries. This allows us to discuss possible phase transitions upon symmetry changes from the SPT perspective. Recent experimental observations of a network of such tilt boundaries suggest that transport through these novel topological kink states might explain the long standing puzzle of sub-gap conductance. Further, recent observation of gap closing and re-opening in gated bi-layer might be the first example of a transition between two distinct SPT's: QVH and LAF.Comment: Improved a discussion of the structural aspects of the tilt boundary. Included a discussion of boundary condition dependence. Added new section on connection to experiment