Wireless sensor networks (WSNs) are typically constituted by a large number of connected sensors (nodes), generally distributed at random on a given surface area. In such largescale networks, the desired global system performance is achieved by gathering local information and decisions collected from each individual node. There exist three fundamental global issues on WSNs that we consider here, namely, full network connectivity, high coverage of the sensing area and reduced power consumption, thus improving on the network lifetime. Full connectivity can be obtained either by increasing the transmission range, at the expense of consuming higher transmission power, or by increasing the number of sensors, i.e. by increasing network costs. Both of them are closely related to global network lifetime, in the sense that the higher the power consumption or the more the number of active sensors present, the shorter the network lifetime (Wang et al., 2007) [1]. Here, we are interested in the minimal number of active nodes required for keeping the network functioning, while the problem of redundancy, i.e. having additional nodes kept in a sleeping mode for a certain period of time, can be implemented afterwards based on the present 'minimal' results. So the main question is, how can one design large-scale random networks in order to have both global connectivity and minimum number of active nodes reducing the total energy consumption? Although these questions have been addressed often in the past, a definite, simple predicting algorithm for achieving these goals does not exist so far. In this paper, we aim to discuss such a scheme and confront it with extensive simulations of random networks generated numerically. Specifically, we study the minimum number of nodes required to achieve full network connectivity, and present an analytical formula for estimating it. The results are in very good agreement with the numerical simulations as a function of transmission range. We also discuss results on how to further diminish network energy consumption by switching off some of the active nodes at random by keeping the connectivity of the whole network. The present results are expected to be useful for the design of more efficient WSNs.

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The network connectivity in dynamic networks depends on a small number of highly mobile nodes. Identifying the influential nodes is one of the most engaging challenges for mobile applications, such as data offloading or worm propagation control. Reachability is an important metric to uncover node influence. Both TRGs (temporal reachability graphs) and CJEGs (critical journey evolving graphs) provide approaches to calculate reachability. Nevertheless, these approaches are only for epidemic scenarios. In practice, due to node privacy or limited battery life, message transmission is, to a certain extent, a probabilistic dissemination. Accordingly, reachability is difficult to exactly determine. As a structure of tight‐knit nodes, a community is born of a coarse‐grained estimation of reachability under a probabilistic propagation scenario. Based on an existing overlapping community detection framework, ie, AFOCS (an unsupervised machine learning algorithm), we propose an evolving overlapping community detection algorithm, ie, EFOCS, and further developed a metric, ie, OR_CEN, to estimate the reachability under the probabilistic propagation scenario. A content delivery experiment showed that OR_CEN accurately reveals the influence of nodes in dynamic networks. Based on OR_CEN, we also propose several target set selection algorithms and discuss their application in mobile data offloading. Analysis and simulation experiments indicated that CBS_OR, the target set selection algorithm based on OR_CEN centrality, has more advantages in scalability and distributed computing than CBS_AFOCS (an algorithm based on an aggregated AFOCS community), TRG_GREEDY (a greedy algorithm based on TRGs) and RANDOM (an algorithm based on a random selection strategy). Moreover, CBS_OR exhibited a significant better offloading effect than the algorithms mentioned earlier.

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