"Clumpiness" Mixing in Complex Networks

Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristic, but accounts only for the clumpiness of the central nodes that are directly connected to each other. The clumpiness coefficient defined in the present paper also takes into account the cases where central nodes are separated by a few links. The definition is based on the node degrees and the distances between pairs of nodes. The clumpiness coefficient together with the assortativity coefficient can define four classes of network. Numerical calculations demonstrate that the classification scheme successfully categorizes 30 real-world networks into the four classes: clumped assortative, clumped disassortative, loose assortative and loose disassortative networks. The clumpiness coefficient also differentiates the Erdos-Renyi model from the Barabasi-Albert model, which the assortativity coefficient could not differentiate. In addition, the bounds of the clumpiness coefficient as well as the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure

"Clumpiness" Mixing in Complex Networks

Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristic, but accounts only for the clumpiness of the central nodes that are directly connected to each other. The clumpiness coefficient defined in the present paper also takes into account the cases where central nodes are separated by a few links. The definition is based on the node degrees and the distances between pairs of nodes. The clumpiness coefficient together with the assortativity coefficient can define four classes of network. Numerical calculations demonstrate that the classification scheme successfully categorizes 30 real-world networks into the four classes: clumped assortative, clumped disassortative, loose assortative and loose disassortative networks. The clumpiness coefficient also differentiates the Erdos-Renyi model from the Barabasi-Albert model, which the assortativity coefficient could not differentiate. In addition, the bounds of the clumpiness coefficient as well as the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure

Modularity and anti-modularity in networks with arbitrary degree distribution

Networks describing the interaction of the elements that constitute a complex system grow and develop via a number of different mechanisms, such as the addition and deletion of nodes, the addition and deletion of edges, as well as the duplication or fusion of nodes. While each of these mechanisms can have a different cause depending on whether the network is biological, technological, or social, their impact on the network's structure, as well as its local and global properties, is similar. This allows us to study how each of these mechanisms affects networks either alone or together with the other processes, and how they shape the characteristics that have been observed. We study how a network's growth parameters impact the distribution of edges in the network, how they affect a network's modularity, and point out that some parameters will give rise to networks that have the opposite tendency, namely to display anti-modularity. Within the model we are describing, we can search the space of possible networks for parameter sets that generate networks that are very similar to well-known and well-studied examples, such as the brain of a worm, and the network of interactions of the proteins in baker's yeast.Comment: 23 pages. 13 figures, 1 table. Includes Supplementary tex

Evolution of networks

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short -- a feature known as the ``small-world'' effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, etc.Comment: 67 pages, updated, revised, and extended version of review, submitted to Adv. Phy

Skeleton and fractal scaling in complex networks

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in-silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.Comment: 4 pages, 2 figures, final version published in PR

Growing network model for community with group structure

We propose a growing network model for a community with a group structure. The community consists of individual members and groups, gatherings of members. The community grows as a new member is introduced by an existing member at each time step. The new member then creates a new group or joins one of the groups of the introducer. We investigate the emerging community structure analytically and numerically. The group size distribution shows a power law distribution for a variety of growth rules, while the activity distribution follows an exponential or a power law depending on the details of the growth rule. We also present an analysis of empirical data from on the online communities, the ``Groups'' in \url{http://www.yahoo.com} and the ``Cafe'' in \url{http://www.daum.net}, which shows a power law distribution for a wide range of group sizes.Comment: 5 figures and 1 tabl

Graphene Grown on Ge(001) from Atomic Source

Among the many anticipated applications of graphene, some - such as transistors for Si microelectronics - would greatly benefit from the possibility to deposit graphene directly on a semiconductor grown on a Si wafer. We report that Ge(001) layers on Si(001) wafers can be uniformly covered with graphene at temperatures between 800{\deg}C and the melting temperature of Ge. The graphene is closed, with sheet resistivity strongly decreasing with growth temperature, weakly decreasing with the amount of deposited C, and reaching down to 2 kOhm/sq. Activation energy of surface roughness is low (about 0.66 eV) and constant throughout the range of temperatures in which graphene is formed. Density functional theory calculations indicate that the major physical processes affecting the growth are: (1) substitution of Ge in surface dimers by C, (2) interaction between C clusters and Ge monomers, and (3) formation of chemical bonds between graphene edge and Ge(001), and that the processes 1 and 2 are surpassed by CH$_{2}$ surface diffusion when the C atoms are delivered from CH$_{4}$. The results of this study indicate that graphene can be produced directly at the active region of the transistor in a process compatible with the Si technology

Dynamic interactions of a conserved enterotoxigenic Escherichia coli adhesin with intestinal mucins govern epithelium engagement and toxin delivery

At present, there is no vaccine for enterotoxigenic Escherichia coli (ETEC), an important cause of diarrheal illness. Nevertheless, recent microbial pathogenesis studies have identified a number of molecules produced by ETEC that contribute to its virulence and are novel antigenic targets to complement canonical vaccine approaches. EtpA is a secreted two-partner adhesin that is conserved within the ETEC pathovar. EtpA interacts with the tips of ETEC flagella to promote bacterial adhesion, toxin delivery, and intestinal colonization by forming molecular bridges between the bacteria and the epithelial surface. However, the nature of EtpA interactions with the intestinal epithelium remains poorly defined. Here, we demonstrate that EtpA interacts with glycans presented by transmembrane and secreted intestinal mucins at epithelial surfaces to facilitate pathogen-host interactions that culminate in toxin delivery. Moreover, we found that a major effector molecule of ETEC, the heat-labile enterotoxin (LT), may enhance these interactions by stimulating the production of the gel-forming mucin MUC2. Our studies suggest, however, that EtpA participates in complex and dynamic interactions between ETEC and the gastrointestinal mucosae in which host glycoproteins promote bacterial attachment while simultaneously limiting the epithelial engagement required for effective toxin delivery. Collectively, these data provide additional insight into the intricate nature of ETEC interactions with the intestinal epithelium that have potential implications for rational approaches to vaccine design