Systematic Topology Analysis and Generation Using Degree Correlations

We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d capture progressively more properties of G at the cost of more complex representation of the probability distribution. Using this series, we can quantitatively measure the distance between two graphs and construct random graphs that accurately reproduce virtually all metrics proposed in the literature. The nature of the dK-series implies that it will also capture any future metrics that may be proposed. Using our approach, we construct graphs for d=0,1,2,3 and demonstrate that these graphs reproduce, with increasing accuracy, important properties of measured and modeled Internet topologies. We find that the d=2 case is sufficient for most practical purposes, while d=3 essentially reconstructs the Internet AS- and router-level topologies exactly. We hope that a systematic method to analyze and synthesize topologies offers a significant improvement to the set of tools available to network topology and protocol researchers.Comment: Final versio

Enhanced suppresion of localization in a continuous Random-Dimer Model

We consider a one-dimensional continuous (Kronig-Penney) extension of the (tight-binding) Random Dimer model of Dunlap et al. [Phys. Rev. Lett. 65, 88 (1990)]. We predict that the continuous model has infinitely many resonances (zeroes of the reflection coefficient) giving rise to extended states instead of the one resonance arising in the discrete version. We present exact, transfer-matrix numerical calculations supporting, both realizationwise and on the average, the conclusion that the model has a very large number of extended states.Comment: 10 pages, 3 Figures available on request, REVTeX 3.0, MA/UC3M/1/9

Delocalization of states in two component superlattices with correlated disorder

Electron and phonon states in two different models of intentionally disordered superlattices are studied analytically as well as numerically. The localization length is calculated exactly and we found that it diverges for particular energies or frequencies, suggesting the existence of delocalized states for both electrons and phonons. Numerical calculations for the transmission coefficient support the existence of these delocalized states.Comment: RevTeX, 12 pages, 2 PS figures adde

Exposing the structure of an Arctic food web

How food webs are structured has major implications for their stability and dynamics. While poorly studied to date, arctic food webs are commonly assumed to be simple in structure, with few links per species. If this is the case, then different parts of the web may be weakly connected to each other, with populations and species united by only a low number of links. We provide the first highly resolved description of trophic link structure for a large part of a high-arctic food web. For this purpose, we apply a combination of recent techniques to describing the links between three predator guilds (insectivorous birds, spiders, and lepidopteran parasitoids) and their two dominant prey orders (Diptera and Lepidoptera). The resultant web shows a dense link structure and no compartmentalization or modularity across the three predator guilds. Thus, both individual predators and predator guilds tap heavily into the prey community of each other, offering versatile scope for indirect interactions across different parts of the web. The current description of a first but single arctic web may serve as a benchmark toward which to gauge future webs resolved by similar techniques. Targeting an unusual breadth of predator guilds, and relying on techniques with a high resolution, it suggests that species in this web are closely connected. Thus, our findings call for similar explorations of link structure across multiple guilds in both arctic and other webs. From an applied perspective, our description of an arctic web suggests new avenues for understanding how arctic food webs are built and function and of how they respond to current climate change. It suggests that to comprehend the community-level consequences of rapid arctic warming, we should turn from analyses of populations, population pairs, and isolated predator-prey interactions to considering the full set of interacting species.Peer reviewe

Cyclic Topology in Complex Networks

We propose a cyclic coefficient $R$ which represents the cyclic characteristics of complex networks. If the network forms a perfect tree-like structure then $R$ becomes zero. The larger value of $R$ represents that the network is more cyclic. We measure the cyclic coefficients and the distributions of the local cyclic coefficient for both various real networks and the representative network models and characterize the cyclic structures of them