# An Efficient Scheme for Constructing Small-World Machine-to-Machine Networks.

07 Jun 2020-pp 1-6

TL;DR: This paper proposes Constrained Link Addition Using high Sensor nodes (CLAUSe) to efficiently construct a few long-ranged links among the chosen high sensor nodes (sensor nodes with at least two interfaces) to reduce end-to-end hop distance in a sparse random M2M network setting, thereby, incorporating the small-world characteristics.

Abstract: Real-world Machine-to-Machine (M2M) networks comprise of power-constrained sensor nodes to collect data of interest and send it to data aggregators for further processing using multi-hop relaying which increases end-to-end transmission delay. However, in many real-world application scenarios such as low latency communication in a 5G network, there is a strict delay deadline that has to be met. In this paper, we propose Constrained Link Addition Using high Sensor nodes (CLAUSe) to efficiently construct a few long-ranged links among the chosen high sensor nodes (sensor nodes with at least two interfaces) to reduce end-to-end hop distance in a sparse random M2M network setting, thereby, incorporating the small-world characteristics.

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TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.

Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

39,297 citations

### "An Efficient Scheme for Constructin..." refers background in this paper

...Addition of a few Long-ranged Links (LLs) among distant high sensor nodes (sensor nodes with at least two interfaces) decreases ETD by transforming a real-world M2M network into a small-world M2M network [2], [3]....

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TL;DR: In this article, three distinct intuitive notions of centrality are uncovered and existing measures are refined to embody these conceptions, and the implications of these measures for the experimental study of small groups are examined.

Abstract: The intuitive background for measures of structural centrality in social networks is reviewed and existing measures are evaluated in terms of their consistency with intuitions and their interpretability. Three distinct intuitive conceptions of centrality are uncovered and existing measures are refined to embody these conceptions. Three measures are developed for each concept, one absolute and one relative measure of the centrality of positions in a network, and one reflecting the degree of centralization of the entire network. The implications of these measures for the experimental study of small groups is examined.

14,757 citations

### "An Efficient Scheme for Constructin..." refers background in this paper

...CC is a network metric which identifies the influence of a node in the context of reachability to other nodes [15]....

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TL;DR: In this paper, a real-space renormalization group transformation for the model is proposed and the scaling form for the average number of degrees of separation between two nodes on the network as a function of the three independent variables is derived.

Abstract: We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a divergent correlation length as the degree of randomness tends to zero. We propose a real-space renormalization group transformation for the model and demonstrate that the transformation is exact in the limit of large system size. We use this result to calculate the exact value of the single critical exponent for the system, and to derive the scaling form for the average number of "degrees of separation" between two nodes on the network as a function of the three independent variables. We confirm our results by extensive numerical simulation.

1,076 citations

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TL;DR: The two greedy criteria used in GMSW are presented, based on which the concept of local importance of nodes is defined, and the algorithm that transforms a network to possess small world properties by adding shortcuts between certain nodes according to their local importance is presented.

Abstract: Robustness is an important and challenging issue in the Internet of Things (IoT), which contains multiple types of heterogeneous networks. Improving the robustness of topological structure, i.e., withstanding a certain amount of node failures, is of great significance especially for the energy-limited lightweight networks. Meanwhile, a high-performance topology is also necessary. The small world model has been proven to be a feasible way to optimize the network topology. In this paper, we propose a Greedy Model with Small World properties (GMSW) for heterogeneous sensor networks in IoT. We first present the two greedy criteria used in GMSW to distinguish the importance of different network nodes, based on which we define the concept of local importance of nodes. Then, we present our algorithm that transforms a network to possess small world properties by adding shortcuts between certain nodes according to their local importance. Our performance evaluations demonstrate that, by only adding a small number of shortcuts, GMSW can quickly enable a network to exhibit the small world properties. We also compare GMSW with a latest related work, the Directed Angulation toward the Sink Node Model (DASM), showing that GMSW outperforms DASM in terms of small world characteristics and network latency.

110 citations

### "An Efficient Scheme for Constructin..." refers methods in this paper

...On the other hand, a greedy model was proposed in [14] to add a few LLs in a heterogeneous IoT network....

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19 Jul 2004TL;DR: An analytical model is developed to analyze the gain in path length reduction by using short cuts in sensor networks and it is found that restricting the knowledge about the wires to 2 hops does not degrade the performance from the case when the authors have global knowledge of all wires.

Abstract: In this paper we investigate the use of wired short cuts in sensor networks. This new paradigm augments a sensor network with a very limited wired infrastructure to improve its overall energy-efficiency. Energy-efficiency is obtained by reduction in average path length. We have developed an analytical model to analyze the gain in path length reduction by using short cuts. We have also conducted extensive simulations to validate our analysis. Our results show that there is an optimal wire length for which the path length reduction is at its maximum, beyond which it decreases. The optimal length is only a small fraction (37.8-50%) of the network diameter. In a network with 1000 nodes uniformly distributed on a disk the path length reduction saturates at 60-70% with 5-24 wires, depending on the location of the sink. Also, we find that restricting the knowledge about the wires to 2 hops does not degrade the performance from the case when we have global knowledge of all wires. These results show promise of the new paradigm.

74 citations

### "An Efficient Scheme for Constructin..." refers background in this paper

...As M2M networks mostly comprise of static or dynamic sensor nodes, wired and wireless LL addition approaches can also be considered [11]–[13]....

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