### Table 3.2: The values for the exponents of the scale-free degree distri- butions of some network models. For directed models, the values for the in-degree and out-degree distributions are given individually. If the reference provides only n = jV j and k, we take m = jEj = nk=2 and round.

2003

Cited by 7

### Table 3.2: Avg. Random Walk Path Lengths for Simulated Graphs (m0 is the size of initial graph in the Scale Free model) Graph Algo. 0.8 0.6 0.5 0.45 0.4 0.35 0.3

2003

### Table 1 Qualitative comparison among characterizations of difierent network models and empirical results on real-world networks.

2006

"... In PAGE 7: ... Thus, some (but not all) small-world networks are also scale-free. Table1 gives a qualitative summary of the various characterizations of networks described... ..."

Cited by 4

### Table 1 Qualitative comparison among characterizations of difierent network models and empirical results on real-world networks.

2006

"... In PAGE 7: ... Thus, some (but not all) small-world networks are also scale-free. Table1 gives a qualitative summary of the various characterizations of networks described... ..."

Cited by 4

### Table 2 before and after evolution.

2004

"... In PAGE 6: ...Figure 8. Output degree distribution of the network in Table2 before and after evolution. Figure 8 shows that the distribution of output connectivity is also shifted towards a more even, scale-free pattern, although this occurs to a lesser extent than in the input connectivity.... ..."

Cited by 4

### Table 1. Network measurements terminology in mathematics/physics and statistics/social network analysis

2007

"... In PAGE 21: ... It also presents an illustrative example to point out the commonalities and differences among regular, random, small world and scale-free networks. Table1 gives an overview of the different terminology used in different scientific disciplines and their interrelations. Obviously, the different disciplines have developed similar techniques in parallel.... ..."

Cited by 1

### Table 1. Network measurements terminology in mathematics/physics and statistics/social network analysis

"... In PAGE 21: ... It also presents an illustrative example to point out the commonalities and differences among regular, random, small world and scale-free networks. Table1 gives an overview of the different terminology used in different scientific disciplines and their interrelations. Obviously, the different disciplines have developed similar techniques in parallel.... ..."

### TABLE II. The scaling exponents characterizing the degree distribution of several scale-free networks, for which P(k) follows a power law (2). We indicate the size of the network, its average degree H20855kH20856, and the cutoff H9260 for the power-law scaling. For directed networks we list separately the indegree (H9253in) and outdegree (H9253out) exponents, while for the undirected networks, marked with an asterisk (*), these values are identical. The columns lreal , lrand , and lpow compare the average path lengths of real networks with power-law degree distribution and the predictions of random-graph theory (17) and of Newman, Strogatz, and Watts (2001) [also see Eq. (63) above], as discussed in Sec. V. The numbers in the last column are keyed to the symbols in Figs. 8 and 9.

2001

Cited by 1

### TABLE II. The scaling exponents characterizing the degree distribution of several scale-free networks, for which P(k) follows a power-law (2). We indicate the size of the network, its average degree hki and the cuto for the power-law scaling. For directed networks we list separately the indegree ( in) and outdegree ( out) exponents, while for the undirected networks, marked with a star, these values are identical. The columns lreal, lrand and lpow compare the average path length of real networks with power-law degree distribution and the prediction of random graph theory (17) and that of Newman, Strogatz and Watts (2000) (62), as discussed in Sect. V. The last column identi es the symbols in Figs. 8 and 9.

2001

Cited by 1

### Table 2.1: Statistics for some real networks. Data are about the total number of nodes n, the total number of connections m, the mean degree z, the mean geodesic length l, the clustering coe cient C and the exponent of the power law degree distribution for scale-free networks. A double value of the power law coe cient means a directed network, where both input and output degree are de ned. The networks showed come from very di erent contexts. The movie actors network is a social network where each node is the representation of a movie actor. Two actors are linked if they have been working together on some movie. Math, physics and biological coauthorship networks are all social network, where scientists are linked together if they are coauthors on the same publication. The Altavista is the network representing the Altavista search engine database, where each node is the representation of a speci c document on the web and a link is the representation of an hyperlink connection between two of such documents. The paper citation is an information network where each nodes represents a speci c paper cataloged by the Institute for the Scienti c Information between 1981 and 1997. Two paper are linked if one has been cited by the other. Follow the network representation of the Internet at level of autonomous systems and the network representing the power grid of the western north America. The last one is a biological network representing the interaction of proteins in the metabolism of the yeast S. Cerevisiae.

2005