Ranking nodes in growing networks: When PageRank fails

Classification of Paper Values Based on Citation Rank and PageRank

Purpose

The number of citations has been widely used to measure the significance of a paper. However, there is a need in introducing another index to determine superiority or inferiority of papers with the same number of citations. We determine superiority or inferiority of papers by using the ranking based on the number of citations and PageRank.

Design/methodology/approach

We show the positive linear correlation between Citation Rank (the ranking of the number of citation) and PageRank. On this basis, we identify high-quality, prestige, emerging, and popular papers.

Findings

We found that the high-quality papers belong to the subjects of biochemistry and molecular biology, chemistry, and multidisciplinary sciences. The prestige papers correspond to the subjects of computer science, engineering, and information science. The emerging papers are related to biochemistry and molecular biology, as well as those published in the journal “Cell.” The popular papers belong to the subject of multidisciplinary sciences.

Research limitations

We analyze the Science Citation Index Expanded (SCIE) from 1981 to 2015 to calculate Citation Rank and PageRank within a citation network consisting of 34,666,719 papers and 591,321,826 citations.

Practical implications

Our method is applicable to forecast emerging fields of research subjects in science and helps policymakers to consider science policy.

Originality/value

We calculated PageRank for a giant citation network which is extremely larger than the citation networks investigated by previous researchers.

Randomizing growing networks with a time-respecting null model

Complex networks are often used to represent systems that are not static but grow with time: People make new friendships, new papers are published and refer to the existing ones, and so forth. To assess the statistical significance of measurements made on such networks, we propose a randomization methodology-a time-respecting null model-that preserves both the network's degree sequence and the time evolution of individual nodes' degree values. By preserving the temporal linking patterns of the analyzed system, the proposed model is able to factor out the effect of the system's temporal patterns on its structure. We apply the model to the citation network of Physical Review scholarly papers and the citation network of US movies. The model reveals that the two data sets are strikingly different with respect to their degree-degree correlations, and we discuss the important implications of this finding on the information provided by paradigmatic node centrality metrics such as indegree and Google's PageRank. The randomization methodology proposed here can be used to assess the significance of any structural property in growing networks, which could bring new insights into the problems where null models play a critical role, such as the detection of communities and network motifs.

Random walks on activity-driven networks with attractiveness

Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously distributed. Here, we present a time-varying network model where each node and the dynamical formation of ties are characterized by these two features. We study how these properties affect random-walk processes unfolding on the network when the time scales describing the process and the network evolution are comparable. We derive analytical solutions for the stationary state and the mean first-passage time of the process, and we study cases informed by empirical observations of social networks. Our work shows that previously disregarded properties of real social systems, such as heterogeneous distributions of activity and attractiveness as well as the correlations between them, substantially affect the dynamical process unfolding on the network.

EIGENVECTOR-BASED CENTRALITY MEASURES FOR TEMPORAL NETWORKS. MULTISCALE MODELING & SIMULATION : A SIAM INTERDISCIPLINARY JOURNAL 2017;15:537-574. [PMID: 29046619 PMCID: PMC5643020 DOI: 10.1137/16m1066142]

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NT × NT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.