By Guoqiang Mao
This ebook introduces a couple of contemporary advancements on connectivity of verbal exchange networks, starting from connectivity of huge static networks and connectivity of hugely dynamic networks to connectivity of small to medium sized networks. This e-book additionally introduces a few functions of connectivity reviews in community optimization, in community localization, and in estimating distances among nodes. The e-book starts off with an summary of the elemental suggestions, types, instruments, and methodologies used for connectivity reports. the remainder of the chapters are divided into 4 components: connectivity of enormous static networks, connectivity of hugely dynamic networks, connectivity of small to medium sized networks, and functions of connectivity studies.
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Additional info for Connectivity of Communication Networks
The infinite network model originated from continuum percolation theory and asymptotic results obtained from the infinite network model have often been applied to the dense and extended networks indiscriminately. In this chapter, through two case studies related to network connectivity on the expected number of isolated nodes and on the vanishing of components of finite order k > 1 respectively, we demonstrate some subtle but important differences between the infinite network model and the dense and extended network models.
An instance Â Ã of G X1 ; gq log Cb ; Ap . 2 Estimating the Number of Isolated Nodes 31 Â of G X ; gr ; A are also valid for the associated instance in G X1 ; gq log Cb C ; Ap Ã . To be more precise, the underlying graphs of these two network instances are isomorphic. Similarly, if we shrink the Euclidean Â distances between Ã all pairs of nodes in a network, which is an instance of G X1 ; gq log p1 Cb C ; Ap , by a factor of , there results an instance of G X ; gr ; A and the two networks again have the Ã Â same connectivity property.
We first give some formal definitions of the concepts and terms. Some of the definitions are not used in this chapter but it may be beneficial to put these definitions in a central place for later use in the book. 20 1 Introduction Definition 15 A walk of length ` between two vertices vi and vj is a sequence of ` edges (not necessarily distinct) where the first edge starts at vi , the last edge ends at vj and the starting vertex of each intermediate edge is the ending vertex of its preceding edge.