Source-linked AI summary
On bibliographic networks
Vladimir Batagelj, Monika Cerinšek
TL;DR
The paper addresses how bibliographic data can be represented as compatible networks and multiplied to obtain derived networks while handling sparsity and normalization. It develops this network-based approach, studies when sparse multiplication preserves sparsity, and illustrates it with Web of Science data on “social network.”
Problem
Bibliographic data involve multiple related network types, while multiplying large sparse networks can require efficient handling and may destroy sparsity.
Method
The paper transforms data tables into compatible two-mode networks, derives networks through multiplication, and studies normalization and sparsity conditions.
Results
The approach produces multiple derived bibliographic networks and establishes sparsity-preserving conditions when high-degree vertices are suitably distributed across the multiplied networks.
Takeaways & Limitations
The approach supports standard social-network analysis of derived one-mode networks and can also be applied to other collections of compatible networks.
Takeaways & Limitations
Multiplication of large sparse networks can be dangerous because the result may no longer be sparse.
Abstract
from arXiv · showhide
In the paper we show that the bibliographic data can be transformed into a collection of compatible networks. Using network multiplication different interesting derived networks can be obtained. In defining them an appropriate normalization should be considered. The proposed approach can be applied also to other collections of compatible networks. We also discuss the question when the multiplication of sparse networks preserves sparseness. The proposed approaches are illustrated with analyses of collection of networks on the topic "social network" obtained from the Web of Science.
1. Introduction
The paper represents bibliographic data as compatible two-mode networks and multiplies networks sharing a common set to derive additional relations. It addresses efficient multiplication for sparse networks and illustrates the approach with Web of Science data on “social network.”
- A collaboration network links authors who co-produced works, with edge weights counting their jointly authored works.
- A works–authors two-mode network records an arc when an author contributed to a work.
- The product W_A^T * W_A computes the corresponding collaboration network from the works–authors matrix W_A.
- A parallel multiplication operation processes only nonzero elements because large-network matrices contain many zero entries.
- Networks such as works–authors and works–keywords can be multiplied through their shared works set to derive author–keyword relations.
- The illustrative Web of Science collection contains 193376 works, 7950 completely described works, 75930 authors, 14651 journals, and 29267 keywords.
2. Two-mode networks and network multiplication
The paper represents data-table properties as compatible two-mode networks and defines their products through matrix multiplication. It develops sparse multiplication and identifies conditions under which products remain sparse, while warning that multiplication can cause density to explode.
- Two-mode networks: A data table contains keyed records whose properties can be represented as two-mode networks linking keys to property values.Finite property ranges yield networks with unit-weight arcs from each key to its associated values.
- Network multiplication: Compatible two-mode networks share an intermediate node set, allowing their product to form a network between the remaining node sets.The product matrix is the standard matrix product, with nonzero entries defining product-network arcs and values defining their weights.
- Network multiplication: With unit input weights, a product entry counts the number of paths between its endpoint nodes through the shared intermediate set.Only terms with nonzero factors contribute to each product entry.
- Sparse multiplication: Sparse multiplication considers only nonzero elements instead of performing standard dense multiplication over all matrix entries.This approach addresses the excessive memory and time requirements of standard representations for large sparse networks.
- Sparsity conditions: Multiplying sparse networks can produce a dense result because intermediate nodes contribute complete subgraphs or two-mode subgraphs.Large degrees at an intermediate node can make constructing one such subgraph quadratic in time and space.
- Sparsity conditions: The product remains sparse when at least one input network has small maximal degree, and more generally when large-degree vertices do not overlap across both networks.The paper also states that small ∆min and d* suffice for sparsity.
3. Collaboration
The paper develops normalized collaboration networks from co-authorship data and uses cores and pS-cores to identify collaborative groups while reducing the dominance of large-author papers.
- 3.1. Co-authorship networks: Author contributions can be normalized by dividing each authorship link by the work's outdegree, assuming equal contribution among authors.The paper notes an alternative using outdeg(p)−1, interpreting the weight as time spent collaborating with each co-author.
- 3.1. Co-authorship networks: Row-normalization divides each outgoing link weight by the sum of weights leaving the same initial node.
- 3.2. The first collaboration network: Standard multiplication produces a symmetric collaboration network whose link weight equals the number of works two authors wrote together.
- 3.2. The first collaboration network: Direct k-cores can be misleading because papers with many authors create complete subgraphs that dominate the highest-order cores.In SN5, cores of orders 20–47 were induced by papers with 21–48 authors rather than necessarily by the most collaborative author groups.
- 3.2. The first collaboration network: pS-cores replace degree with the total weight of links within the candidate group, and the level-20 core requires each author to have at least 20 internal collaborations.The reported core retains strongly collaborating groups while large cliques disappear in the normalized third collaboration network.
- 3.3. The second collaboration network: The paper introduces contribution-based collaboration weights and indices, including self-contribution, collaborativness, and self-sufficiency measures.For the third collaboration network, weights are symmetric, total work contribution is conserved, and the average self-sufficiency index is 1.
4. Derived networks
The paper derives multiple bibliographic networks from citation, authorship, and keyword relations, using normalized weights to reduce distortions from highly connected works. These networks reveal citation, collaboration, and author-group structures in the SN5 data.
- Bibliographic coupling and co-citation: Normalization is introduced because works with many citations, especially review papers, can otherwise exert disproportionate influence.
- Bibliographic coupling and co-citation: Normalized bibliographic coupling values lie in [0, 1], are symmetric, and equal 1 when two works reference the same works.
- Bibliographic coupling and co-citation: Bibliographic coupling counts works cited by both papers, while co-citation counts works citing both papers.
- Author-based derived networks: Author citation, author co-citation, and author-keyword networks encode cited works, jointly cited works, and keyword use by authors, respectively.
- Author-based derived networks: The authors’ citation network weights links by how often works co-authored by one author cite works co-authored by another, as shown in Figure 5.
- Observed network structure: In Ca(SN5), the largest island contains mainstream social-network researchers, while other islands include physicists, medical researchers, and education and psychology groups.
- Observed network structure: Most remaining islands are star-like, typically centered on a professor and their PhD students.
5. Conclusions
The paper concludes that bibliographic data can be transformed into compatible networks and multiplied to obtain derived networks, provided their weights are appropriately normalized. These networks support standard SNA, two-mode, multilevel, and temporal analyses.
- Bibliographic data can be transformed into a collection of compatible networks that share sets and can be multiplied to produce derived networks.
- Appropriate normalization is needed when defining weights in the derived networks.
- Most derived networks are one-mode networks suitable for standard SNA methods, while two-mode networks support cores, hubs and authorities, and 4-rings islands.
- Citation and other Web of Science networks can be transformed into temporal networks using publication-year partitions and time slices.
- Partitions and class shrinking allow analyses at levels such as institutions, countries, and academic fields, while class extraction narrows the network to a selected area.