The underwater acoustic channel is characterized by a path loss that depends not only on the transmission distance, but also on signal frequency. Signals transmitted from one user to another over a distance _l_ are subject to a power loss of _l_^−α_a_(_f_)^{−<em>l</em>}. Although a terrestrial radio channel can be modeled similarly, the underwater acoustic channel has different characteristics. The spreading factor α, related to the geometry of propagation, has values in the range 1⩽α⩽2. The absorption coefficient _a_(_f_) is a rapidly increasing function of frequency: it is three orders of magnitude greater at 100 kHz than at a few hertz. Existing results for capacity of radio wireless networks correspond to scenarios for which _a_(_f_)=1, or a constant greater than one, and α⩾2. These results cannot be applied to underwater acoustic networks in which the attenuation varies over the system bandwidth. We use a water-filling argument to assess the minimal transmission power and optimal transmission band as functions of the link distance and desired data rate, and study the capacity scaling laws under this model. We show that the transport capacity increases at most at a rate <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="uinm_a_720481_o_ilm0001.gif"></inline-graphic>, where _W_₀ represents the branch zero of the Lambert W function, for the cases in which the transmission band is either fixed a priori or assigned in relation to the transmission distance. This means that the transport capacity increases much more slowly than that of multihop routing in wireless scenarios, which is bounded by _O_(_n_^1/2). Finally, we show that scaling the frequency of the transmission band with the number of nodes provides a means to exploit characteristics of the acoustic channel in order to overcome the previous pessimistic results.

In this paper, we consider backpressure-based control for wireless multihop networks with time-correlated arrivals. The arrival process considered in this work is fairly general in the sense that it may exhibit short- or long-range dependence depending on the asymptotic shape of the autocorrelation function. We first show that the original backpressure policy stabilizes the network whenever the arrival rate vector is inside the stability region no matter whether the arrivals are i.i.d. or time-correlated but with monotonically decreasing autocorrelation functions. Apart from stability, the effect of correlations appears in the upper bound on average network delay. After that, we move to the case that the arrival rate vector is possibly outside the stability region. To deal with such a case, we take the method of joint flow control and backpressure policy that is known for i.i.d. arrivals to perform arbitrarily close to the utility-optimal throughput point with a corresponding tradeoff in average network delay. The tradeoff is redefined for the network with time-correlated arrivals.

Despite the extreme success of spectral graph theory, there are relatively few papers applying spectral analysis to hypergraphs. Chung first introduced Laplacians for regular hypergraphs and showed some useful applications. Other researchers have treated hypergraphs as weighted graphs and then studied the Laplacians of the corresponding weighted graphs. In this paper, we aim to unify these very different versions of Laplacians for hypergraphs. We introduce a set of Laplacians for hypergraphs through studying high-order random walks on hypergraphs. We prove that the eigenvalues of these Laplacians can effectively control the mixing rate of high-order random walks, the generalized distances/diameters, and the edge expansions.

We propose and analyze a class of evolving network models suitable for describing a dynamic topological structure. Applications include telecommunication, online social behavior, and information processing in neuroscience. We model the evolving network as a discrete-time Markov chain and study a very general framework in which edges conditioned on the current state appear or disappear independently at the next time step. We show how to exploit symmetries in the microscopic, localized rules in order to obtain conjugate classes of random graphs that simplify analysis and calibration of a model. Further, we develop a mean field theory for describing network evolution. For a simple but realistic scenario incorporating the triadic closure effect that has been empirically observed by social scientists (friends of friends tend to become friends), the mean field theory predicts bistable dynamics, and computational results confirm this prediction. We also discuss the calibration issue for a set of real cellphone data, and find support for a block model in which individuals are assigned to one of two distinct groups having different within-group and across-group dynamics.

Hierarchical organization is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organization. However, in many real-world networks, such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data are collated, the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network to reveal this type of hierarchy. In doing so, we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random-graph model. This random-graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node-ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google's PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically.

Network visualization tools offer features enabling a variety of analyses to satisfy diverse requirements. Considering complexity and diversity of data and tasks, there is no single best layout, no single best file format or visualization tool: one size does not fit all. One way to cope with these dynamics is to support multiple scenarios and workflows. NAViGaTOR (Network Analysis, Visualization & Graphing TORonto) offers a complete system to manage diverse workflows from one application. It allows users to manipulate large graphs interactively using an innovative graphical user interface (GUI) and through fast layout algorithms with a small memory footprint. NAViGaTOR facilitates integrative network analysis by supporting not only visualization but also visual data mining.

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This paper presents a cache-aware Bloom-filter algorithm with improved cache behavior and lower false-positive rates compared to prior work. The algorithm relies on the power-of-two choice principle to provide a better distribution of set elements in a blocked Bloom filter. Instead of choosing a single block, we insert new elements into the less-loaded of two blocks to achieve a low false-positive rate while performing only two memory accesses on each insert or query operation. The paper also discusses an optimization technique to balance cache effectiveness with the false-positive rate to fine-tune the Bloom-filter properties.

Random graphs with given degrees are a natural next step in complexity beyond the Erdős–Renyi model, yet the degree constraint greatly complicates simulation and estimation. We use an extension of a combinatorial characterization due to Erdős and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows for surprisingly efficient sequential importance sampling. The resulting probabilities are easily computed on the fly, allowing the user to reweight estimators appropriately, in contrast to some ad hoc approaches that generate graphs with the desired degrees but with completely unknown probabilities. Applications are given, including simulating an ecological network and estimating the number of graphs with a given degree sequence.

Internet is a complex network composed by several networks: the Autonomous Systems, each one designed to transport information efficiently. Routing protocols aim to find paths between nodes whenever it is possible (i.e., the network is not partitioned), or to find paths verifying specific constraints (e.g., a certain QoS is required). As connectivity is a measure related to both of them (partitions and selected paths) this work provides a formal lower bound to it based on core-decomposition, under certain conditions, and low complexity algorithms to find it. We apply them to analyze maps obtained from the prominent Internet mapping projects, using the LaNet-vi open-source software for its visualization.