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57
L.: A fair history of the Web? Examining country balance
 in the Internet Archive. Library & Inf. Sci. Research
, 2004
"... The Internet Archive, an important initiative that maintains a record of the evolving Web, has the promise of being a key resource for historians and those who study the Web itself. The Archive’s goal is to index the whole Web without making any judgments about which pages are worth saving. The pote ..."
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The Internet Archive, an important initiative that maintains a record of the evolving Web, has the promise of being a key resource for historians and those who study the Web itself. The Archive’s goal is to index the whole Web without making any judgments about which pages are worth saving. The potential importance of the Archive for longitudinal and historical Web research leads to the need to evaluate its coverage. This article focuses upon whether there is an international bias in its coverage. The results show that there are indeed large national differences in the Archive’s coverage of the Web. A subsequent statistical analysis found differing national average site ages and hyperlink structures to be plausible explanations for this uneven coverage. Although the bias is unintentional, researchers using the Archive in the future need to be aware of this problem.
The degree sequences and spectra of scalefree random graphs
, 2004
"... We investigate the degree sequences of scalefree random graphs. We obtain a formula for the limiting proportion of vertices with degree d, confirming nonrigorous arguments of Dorogovtsev et al [10]. We also consider a generalisation of the model with more randomisation, proving similar results. Fi ..."
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We investigate the degree sequences of scalefree random graphs. We obtain a formula for the limiting proportion of vertices with degree d, confirming nonrigorous arguments of Dorogovtsev et al [10]. We also consider a generalisation of the model with more randomisation, proving similar results. Finally, we use our results on the degree sequence to show that for certain values of parameters localised eigenfunctions of the adjacency matrix can be found.
Rankbased attachment leads to power law graphs
 INTERNET MATHEMATICS, SUBMITTED
"... We investigate the degree distribution resulting from graph generation models based on rankbased attachment. In rankbased attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is proportional to its rank raised to the power −α, for some α ∈ (0, 1 ..."
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We investigate the degree distribution resulting from graph generation models based on rankbased attachment. In rankbased attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is proportional to its rank raised to the power −α, for some α ∈ (0, 1). Through a rigorous analysis, we show that rankbased attachment models lead to graphs with a power law degree distribution with exponent 1 + 1/α whenever vertices are ranked according to their degree, their age, or a randomly chosen fitness value. We also investigate the case where the ranking is based on the initial rank of each vertex; the rank of existing vertices only changes to accommodate the new vertex. Here, we obtain a sharp threshold for power law behaviour. Only if initial ranks are biased towards lower ranks, or chosen uniformly at random, we obtain a power law degree distribution with exponent 1 + 1/α. This indicates that the power law degree distribution often observed in nature can be explained by a rankbased attachment scheme, based on a ranking scheme that can be derived from a number of different factors; the exponent of the power law can be seen as a measure of the strength of the attachment.
Highdimensional random Apollonian networks
 Phys. A
"... We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with smallworld and scalefree characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of ..."
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We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with smallworld and scalefree characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of the network. The values obtained for these parameters are in good agreement with simulation results and comparable to those coming from real networks. We prove also analitically that the average path length of the networks increases at most logarithmically with the number of vertices.
Modeling the Evolution of Degree Correlation in ScaleFree Topology Generators
"... In this paper, we examine the asymptotic behavior of degree correlation (i.e., the joint degree distribution of adjacent nodes) in several scalefree topology generators GED [14], PLRG [1], GLP [11], BA [4], AB [2]. We present a unifying analytical framework that allows tractable analysis of degree ..."
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In this paper, we examine the asymptotic behavior of degree correlation (i.e., the joint degree distribution of adjacent nodes) in several scalefree topology generators GED [14], PLRG [1], GLP [11], BA [4], AB [2]. We present a unifying analytical framework that allows tractable analysis of degree correlation in all studied models and derive asymptotic formulas of two degree correlation metrics – assortativity and clustering. Our results indicate that all studied generators become uncorrelated as graph size increases, which is inconsistent with timeinvariance of these metrics in real networks such as the Internet [37], [49], [51]. Since the class of degreebased generators is incapable of reproducing evolving characteristics of the Internet, we study three other models that evolve graphs using different rules than preference of degree (e.g., based on random walks [51], optimization [18], and geometry [24]) and show using simulations that these models are much more viable alternatives for replicating the complex structure of Internetlike graphs.
Modeling for evolving biological networks with scalefree connectivity, hierarchical modularity, and disassortativity
, 2006
"... ..."
Scalefree overlay topologies with hard cutoffs for unstructured peertopeer networks
 In Proceedings of IEEE ICDCS
, 2007
"... In unstructured peertopeer (P2P) networks, the overlay topology (or connectivity graph) among peers is a crucial component in addition to the peer/data organization and search. Topological characteristics have profound impact on the efficiency of search on such unstructured P2P networks as well as ..."
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In unstructured peertopeer (P2P) networks, the overlay topology (or connectivity graph) among peers is a crucial component in addition to the peer/data organization and search. Topological characteristics have profound impact on the efficiency of search on such unstructured P2P networks as well as other networks. A key limitation of scalefree (powerlaw) topologies is the high load (i.e. high degree) on very few number of hub nodes. In a typical unstructured P2P network, peers are not willing to maintain high degrees/loads as they may not want to store large number of entries for construction of the overlay topology. So, to achieve fairness and practicality among all peers, hard cutoffs on the number of entries are imposed by the individual peers, which limits scalefreeness of the overall topology. Thus, it is expected that efficiency of the flooding search reduces as the size of the hard cutoff does. We investigate construction of scalefree topologies with hard cutoffs and effect of these hard cutoffs on the search efficiency. 1.
Scalable routing easy as pie: A practical isometric embedding protocol
 in Network Protocols (ICNP), 2011 19th IEEE International Conference on, 2011
"... We present PIE, a scalable routing scheme that achieves 100 % packet delivery and low path stretch. It is easy to implement in a distributed fashion and works well when costs are associated to links. Scalability is achieved by using virtual coordinates in a space of concise dimensionality, which ena ..."
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We present PIE, a scalable routing scheme that achieves 100 % packet delivery and low path stretch. It is easy to implement in a distributed fashion and works well when costs are associated to links. Scalability is achieved by using virtual coordinates in a space of concise dimensionality, which enables greedy routing based only on local knowledge. PIE is a general routing scheme, meaning that it works on any graph. We focus however on the Internet, where routing scalability is an urgent concern. We show analytically and by using simulation that the scheme scales extremely well on Internetlike graphs. In addition, its geometric nature allows it to react efficiently to topological changes or failures by finding new paths in the network at no cost, yielding better delivery ratios than standard algorithms. The proposed routing scheme needs an amount of memory polylogarithmic in the size of the network and requires only local communication between the nodes. Although each node constructs its coordinates and routes packets locally, the path stretch remains extremely low, even lower than for centralized or less scalable stateoftheart algorithms: PIE always finds short paths and often enough finds the shortest paths. Abstract — 1 I.