This paper investigates two fundamental characteristics of a wireless multihop network: its minimum node degree and its k–connectivity. Both topology attributes depend on the spa-tial distribution of the nodes and their transmission range. Using typical modeling assumptions — a random uniform

Wireless Sensor Network (WSN) is widely used for monitoring and gathering data in an autonomous fashion. Since sensors are small and power constrained devices, it is the most important to minimize the energy consumption. We propose Node Degree Based Clustering (NDBC) for enhancing life time

The Internet topology data collected through traceroute exploration has been extensively studied in the past. In particular, a remarkable property of the Internet, the power-law shape of node degree distribution, drew the attention of the research community. Several studies have since questioned

according to a hybrid of the node residual energy and a secondary parameter, such as node proximity to its neighbors or node degree. HEED terminates in Oð1Þ iterations, incurs low message overhead, and achieves fairly uniform cluster head distribution across the network. We prove that, with appropriate

to estimate node degree on portions of the interactome assayed by bait-prey technologies. This approach yields substantial improvement in degree estimation over the current practice which naïvely sums observed edges. Accurate modeling of observed data in relation to true but unknown parameters of interest

We prove that both the NP-completeness of the nonplanar deletion decision problem and the Max SNP-hardness of the nonplanar deletion problem remain true even for cubic graphs. We prove that the class of graphs with splitting number less than or equal to a fixed k is minor closed, which implies the existence of a corresponding polynomial-time recognition algorithm.

A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collision-free configurations and whose

We design low-density parity-check (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming

number of systems, such as the World Wide Web (www) [3–5], Internet [6], social networks [7] or a cell [8], display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected by even unrealistically high failure rates. However,

contain a densely connected core of high-degree nodes; and that this core links small groups of strongly clustered, low-degree nodes at the fringes of the network. Finally, we discuss the implications of these structural properties for the design of social network based systems.