The academic social network

Abstract

By means of their academic publications, authors form a social network. Instead of sharing casual thoughts and photos (as in Facebook), authors select co-authors and reference papers written by other authors. Thanks to various efforts (such as Microsoft Academic Search and DBLP), the data necessary for analyzing the academic social network is becoming more available on the Internet. What type of information and queries would be useful for users to discover, beyond the search queries already available from services such as Google Scholar? In this paper, we explore this question by defining a variety of ranking metrics on different entities—authors, publication venues, and institutions. We go beyond traditional metrics such as paper counts, citations, and h-index. Specifically, we define metrics such as influence, connections, and exposure for authors. An author gains influence by receiving more citations, but also citations from influential authors. An author increases his or her connections by co-authoring with other authors, and especially from other authors with high connections. An author receives exposure by publishing in selective venues where publications have received high citations in the past, and the selectivity of these venues also depends on the influence of the authors who publish there. We discuss the computation aspects of these metrics, and the similarity between different metrics. With additional information of author-institution relationships, we are able to study institution rankings based on the corresponding authors’ rankings for each type of metric as well as different domains. We are prepared to demonstrate these ideas with a web site (http://pubstat.org) built from millions of publications and authors.

Appendices

Appendix 1: The PageRank algorithm

Given a graph $G=(V,E)$, the PageRank algorithm can be considered as a random walk starting from any node along the edges. After an infinite number of steps, the probability that a node is visited is the PageRank value of that node.

More formally, the probability distribution of visiting each node can be derived by solving a Markov Chain. The transition matrix C’s entries $c_{ij}$ ($i,j=1,2,\dots , n$) represent the transition probability that the random walk will visit node j next given that it is currently at node i. Thus, $c_{ij}$ can be expressed as

$$\begin{aligned} c_{ij} = {\text {Prob}}(j|i) = \frac{e_{ij}}{\sum _k e_{ik}} \end{aligned}$$

(1)

where $e_{ij}$ is from the adjacency matrix for the graph G. If G is the citation graph, for example, then $e_{ij}=1$ if paper i cites paper j; else $e_{ij}=0$.

In general, C is a substochastic matrix with rows summing to either 0 (dangling nodes, see also Brin and Page 1998, for example, representing papers with citing no other papers) or 1 (normal nodes, or papers). For each dangling node, the corresponding row is replaced by $\frac{1}{n}{\mathbf {e}}$, so that C becomes a stochastic matrix.

In order to ensure the Markov Chain C is irreducible, hence a solution is guaranteed to exist, C is further transformed as follows:

$$\begin{aligned} \widetilde{C} = \alpha C + (1-\alpha ){\mathbf {e}}{\mathbf {v}}^{\mathrm{{T}}}, \;\;\alpha \in (0,1). \end{aligned}$$

(2)

Here, ${\mathbf {e}}$ is a special column vector with all 1s, and of dimension n.

In Eq. (2), ${\mathbf {v}}\in {\mathcal {R}}^{n}$ is a probability vector (i.e., its values are between 0 and 1, and sum to 1). It is referred to as the teleportation vector, which can be used to configure some bias into the random walk. For our purposes, we let ${\mathbf {v}} = 1/n{\mathbf {e}}$ as the default setting.

Now, according to the Perron–Frobenius Theorem (Langville and Meyer 2009; Meyer 2000), matrix $\widetilde{C}$ is stochastic, irreducible, and aperiodic, and the equation

$$\begin{aligned} \pi ^{\mathrm{{T}}}=\alpha \pi ^{\mathrm{{T}}}C+(1-\alpha )\frac{1}{n}{\mathbf {e}}^{\mathrm{{T}}},\;\;\alpha \in (0,1) \end{aligned}$$

(3)

which can be solved by iteration methods in practice.

Appendix 2: Definition of metrics in matrix form

We list the matrix form for the five metrics discussed in the previous sections in Table 18.

Table 18 Notations and derivations of the ranking metrics