On the relationships between topological measures in real-world networks

Abstract

Over the past several years, a number of measures have been introduced to characterize the topology of complex networks. We perform a statistical analysis of real data sets, representing the topology of different realworld networks. First, we show that some measures are either fully related to other topological measures or that they are significantly limited in the range of their possible values. Second, we observe that subsets of measures are highly correlated, indicating redundancy among them. Our study thus suggests that the set of commonly used measures is too extensive to concisely characterize the topology of complex networks. It also provides an important basis for classification and unification of a definite set of measures that would serve in future topological studies of complex networks.

Inferring a Drive-Response Network from Time Series of Topological Measures in Complex Networks with Transfer Entropy

“…The correlations between topological measures strongly depend on the graph under study [14], and results from these studies differ greatly. Some of them argue that most of the measures are strongly correlated and thus can be redundant, while others argue that these correlations are not strong overall.…”

“…Jamakovic et al [14] collected data from 20 real-life networks from technological, social, biological and linguistic systems, and calculated the correlation coefficients between 14 topological measures. It was observed that subsets of measures were highly correlated, and Principal Component Analysis (PCA) showed that only three dimensions were enough to retain most of the original variability in the data, capturing more than 99% of the total data set variance.…”

“…The relationship of topological measures has been a research topic for several years [4,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], and there mainly exist two paradigms, i.e., analytical modeling and data-driven modeling. For a few topological measures of model networks, i.e., networks generated with certain algorithm, some analytical interrelationships are found.…”

Towards Trusted Services: Result Verification Schemes for MapReduce

“…Apparently, the weighted scheme outperforms the naive one. For the Internet, Jamakovic and Uhlig [16] concluded that the in-degrees of the Internet follow a power law distribution f (x) = ax −γ , x ∈ [0, inf). Under this circumstance, we can conduct a similar derivation and obtain the following results.…”

“…According to Jamakovic and Uhlig [16], in a regulatory network, the in-degrees follow an exponential distribution. Let's assume that x follows an exponential distribution, we have, f (x) = K exp(−Kx), x ∈ [0, inf).…”