Ranking stability and super-stable nodes in complex networks

Abstract

Pagerank, a network-based diffusion algorithm, has emerged as the leading method to rank web content, ecological species and even scientists. Despite its wide use, it remains unknown how the structure of the network on which it operates affects its performance. Here we show that for random networks the ranking provided by pagerank is sensitive to perturbations in the network topology, making it unreliable for incomplete or noisy systems. In contrast, in scale-free networks we predict analytically the emergence of super-stable nodes whose ranking is exceptionally stable to perturbations. We calculate the dependence of the number of super-stable nodes on network characteristics and demonstrate their presence in real networks, in agreement with the analytical predictions. These results not only deepen our understanding of the interplay between network topology and dynamical processes but also have implications in all areas where ranking has a role, from science to marketing.

Identifying the influential spreaders in multilayer interactions of online social networks

“…Consequently, the PageRank algorithm is an unreliable measurement for OSNs. Moreover, the finding of this paper reconfirmed that the accomplishment of PageRank in web network, while it failed in OSNs, was due to the unintentional result of the scale-free nature of the web graph [62]. If the web graph was an exponential network, the ranking generated by PageRank would have been unreliable given the incompleteness of the web graph [62].…”

“…This is due to the topology perturbations of the retweet network, which affect the ranking values provided by the ranking algorithms. This effect has been observed by the diverse imprecision functions values and recognition rates of the ranking algorithms applied to retweet network [62]. In contrary to the proposed weighted aggregated topological network representation, this has provided informative network data, which result in comparable low imprecision function and high recognition rate for all algorithms in both datasets.…”

“…The top spreaders were limited to those who have a bidirectional relationship. From the result Figures 5, 6,7, and 8, it is observed that the PageRank has failed to detect influential spreaders in most of the studied network, as both datasets represent incomplete network data of OSNs and the measurements given by PageRank are responsive to perturbations in network topology, rendering it unreliable for incomplete or noisy networks [62]. However, the complete OSN structure is unavailable due to the inherent limitations of OSNs caused by API restrictions and user privacy.…”

Approximate entropy of network parameters

“…If we are drawing the degrees deg(v) of nodes v ∈ {1,...,N } then E(d 1 − d N ) = E 1 − E N can be computed for the scale-free degree distribution (we have E N = 1 almost surely) given approximately (following Ghoshal-Barabási [35]) by…”

Promoting information spreading by using contact memory

“…Promoting spreading speed and understanding its effects in the outbreak size of the reached nodes are two important features to study in both theoretical and empirical aspects. Theoretically existing studies found that promoting the spreading dynamics could induce distinct critical phenomena with different outbreak thresholds and critical exponents [8]. Practically speaking, promoting the spreading dynamics could shed some lights on the propagation of information [9][10][11], marketing management [12,13], disease spreading [14][15][16][17][18], etc.…”