Using data network metrics, graphics, and topology to explore network characteristics

Abstract

Yehuda Vardi introduced the term network tomography and was the first to propose and study how statistical inverse methods could be adapted to attack important network problems (Vardi, 1996). More recently, in one of his final papers, Vardi proposed notions of metrics on networks to define and measure distances between a network's links, its paths, and also between different networks (Vardi, 2004). In this paper, we apply Vardi's general approach for network metrics to a real data network by using data obtained from special data network tools and testing procedures presented here. We illustrate how the metrics help explicate interesting features of the traffic characteristics on the network. We also adapt the metrics in order to condition on traffic passing through a portion of the network, such as a router or pair of routers, and show further how this approach helps to discover and explain interesting network characteristics.

Optimization processes of tangible and intangible networks through the Laplace problems for regular lattices with multiple obstacles along the way

“…C omplex networks are networks whose structure is irregular, complex and which evolves over time and are used in various branches of science and technology, as in biochemistry, in the study of interactions in quantum field theory, in study of IT processes, topologies in geographical databases [1] and also on the web, in social networks such as Facebook and Linkedin and in the Google model. The same term "complex" derives from the latin cum (together) -plexus (intertwined), "intertwined together": it highlights that a complex network system is composed of a set of parts connected together and "intertwined" in such a way that the final result (the effect produced) is different from the sum of the constituent parts.…”

“…In general, the problem of flow at minimum cost consists in to find an admissible flow distribution on the network G=(N,L) such that the total cost is minimal. If we indicate the incidence matrix of the network with A G with b=[b (1),b(2),...,b(n)] T the supply/demand vector, with R m the cost vector and with l ∈ (R m ) + ,u ∈ (R m ) + the vectors whose components represent the lower limit and the capacity of the corresponding arc, the minimum cost flow problem can be analytically defined through the following system:…”

“…Let ℜ (a,b,c) be the regular lattice with fundamental cell is as in Figure 8. Denoting with C 0 (1) the fundamental cell, we have:…”

“…The cell C 0 (1) have six obstacles that are squares with diagonal of length c with c<min(a,b). Considering a segment s of random position and of length l with c<l<min(a,b), we want compute the probability that this segment intersects a side of lattice.…”

Statistical Aspects of the Analysis of Data Networks

“…We have developed and used visualization tools in an iterative manner to supplement the formal techniques (Adhikari et al 2006;Adhikari, Denby, Landwehr, and Meloche 2007). A static medium such as a journal article obviously constrains our ability to illustrate the features of a visualization tool.…”