Abstract:
Analysis of spectrum density and SLS(signless Laplacian spectra) on router-level macroscopic toplogy was performed.Firstly,we found in experiments that five analysis results of spectrum density on five sampling topologies showed highly similarity proving that Internet is a system of self-similarity as well as the ability for sampling topology to resemble the whole Internet topology.Secondly,obvious difference between the spectrum density analysis results of sampling topology,ER graph and BA graph indicated ...

Abstract:
Being a huge system, Internet topology structure is very complex. It can’t be treated as a plane simply, and its hierarchy must be analyzed. We used the k-core decomposition to disentangle the hierarchical structure of Internet Router-level topology. By analyzing the router-lever Internet topology measuring data from CAIDA (The Cooperative Association for Internet Data Analysis) ,we studied the characteristics of the nodes in the inner hierarchy and outer hierarchy respectively. The frequency-degree power law of the nodes which core-ness is lower and the regionally distribution of the nodes which coreness is higher were concluded. At last, the topology of every hierarchy was described by giving their figures. These descriptions can provide a valuable reference for modeling on the Internet topology.

Abstract:
We present a statistical analysis of different metrics characterizing the topological properties of Internet maps, collected at two different resolution scales: the router and the autonomous system level. The metrics we consider allow us to confirm the presence of scale-free signatures in several statistical distributions, as well as to show in a quantitative way the hierarchical nature of the Internet. Our findings are relevant for the development of more accurate Internet topology generators, which should include, along with the scale-free properties of the connectivity distribution, the hierarchical signatures unveiled in the present work.

Abstract:
Modeling of Internet topology structure is studied in this paper. First, measuring results of Internet topology from CAIDA monitors have been used to produce a complete topology sample. With this sample, research approaches of the frequency-degree power-law, degree-rank power-law and CCDF(d)-degree power-law have been studied to outline the network power-law properties. The frequency-degree power-law relationship is found to be with a power exponent of 2.1406. The degree-rank power-law, however, is found to have two phases of power-law relationships with power-exponents of 0.29981 and 0.84639 respectively. Then, we improved the traditional BA model to construct an Internet topology model (Improved BA model, IBA model), and optimized the IBA model in Genetic Algorithm by the power-exponents gained from frequency-degree power and degree-rank power-law analyses in the paper. Generation algorithm for the IBA model was given at last.

Abstract:
The As-level topology is a hotspot of the recent reseaches. We can understand the centralization of the network clearly by researching the evolvement trend of the Internet macroscopic topology. The massive data we use in this paper is from CAIDA (The Cooperative Association for Internet Data Analysis) Skitter project. And the time span of the data is from July, 2001 to January, 2008. This paper introduces the background of the AS-level topology at first, then carries out the evolvement of degree, core and layer. It is believed that the influence of the top-degree nodes on the other nodes decreases and the centralization of network is going to fall off with the decrease of the core. And the nucleus status of network declines.

Abstract:
Cross-correlation evaluation model, CCEM, was mainly studied to evaluate how much two different topologies are similar to each other in a quantitative way, and further used in evaluating whether a topology by an Internet topology model is close to real Internet or not. SLS (Signless Laplacian Spectra), is used to quantitatively identify the topology properties of the Internet generated by the model and the Internet out of real measuring. SLS eigenvectors could be gained out of this procedure, then a cross-correlation calculation was performed on the eigenvectors to give the difference identification in a quantitative way. With this, a recommended way of using the CCEM within a Genetic Algorithm was finally given.

Abstract:
Because the statistical method with multi-angle and multi-measurement has many problems,a method to depict the overall Internet topology characteristics by using network fractal dimension was proposed in the paper.With the basement of the traditional fractal theory,combined with the self-similarity of Internet topology,the related concepts of the network topology dimension were given.By the mapping from Euclidean space to topology structure,the network topology dimension had been analyzed deeply and then th...

Abstract:
A detailed understanding of the structural properties of Internet topology will benefit the further design and development of the Internet. It seems infeasible to study the whole Internet at router level due to its extremely large size and the difficulty in obtaining a whole topology at this level. Studying each national or continental Internet service provider (ISP) topology individually becomes an alternative method for this goal. In this paper, the measured China Education and Research Network topology, a nationwide ISP topology, is basically taken as an example. The results of mapping the topology from multiple vantage points are briefly presented. The properties of the degree distribution, large eigenvalues, and the spectral density of the measured topology graphs are analyzed. The characteristics of the signless Laplacian spectra (SLS), the normalized Laplacian spectra (NLS), and the clustering coefficients of the measured graphs are also presented. The results suggest that some power laws indeed hold in some large-scale ISP topologies; in contrast to the case of autonomous system level topologies, the power law fit is not the best choice for some ISP topologies in terms of the complementary cumulative distribution function of the degree; some real ISP topologies are a kind of scale-free graphs which are not consistent with the Barabási-Albert (BA) growth model; router level topologies are distinguishable in terms of the SLS or the NLS; router level Internet topology may have developed over time following a different set of growth processes from those of the BA model.

Abstract:
This paper presents the basic concept of topology's properties and modeling metrics; categorizes and analyzes both AS-level models and router-lever models. Moreover, this paper summarizes current research achievements on Internet topology's modeling, especially at the router-level. Finally, it identifies future directions and open problems of the topology modeling research.

Abstract:
Network generators that capture the Internet's large-scale topology are crucial for the development of efficient routing protocols and modeling Internet traffic. Our ability to design realistic generators is limited by the incomplete understanding of the fundamental driving forces that affect the Internet's evolution. By combining the most extensive data on the time evolution, topology and physical layout of the Internet, we identify the universal mechanisms that shape the Internet's router and autonomous system level topology. We find that the physical layout of nodes form a fractal set, determined by population density patterns around the globe. The placement of links is driven by competition between preferential attachment and linear distance dependence, a marked departure from the currently employed exponential laws. The universal parameters that we extract significantly restrict the class of potentially correct Internet models, and indicate that the networks created by all available topology generators are significantly different from the Internet.