## 2 Bibliometric Analysis
### Bibliometric Networks  
Among others, bibliometric analyses deal with networks of bibliographic entities. _Bibliometric networks_ describe affiliations or similarities of bibliographic entities, such as academic publications, authors, journals, institutions, countries, or keywords, and are used to find groups of similar entities and relations to other entities or groups. In 1965, [PERSON] [18] investigated the citation behavior of journal articles and started the field of bibliometric networks by depicting a network of journal articles. A minimalistic example of an article network is shown in Figure 2. [PERSON]'s network shows journal articles as nodes and citations among the articles (sometimes also called references, but used synonymously here) as directed edges, i.e., there is an edge from node one to node two if node one cites node two. In case of the shown network, articles one and two both cite article three. Mathematically, an article network can be represented by the adjacency matrix of its underlying directed graph. Based on the idea of [18], different bibliometric networks arose. In general, there are two groups of bibliometric networks: affiliation networks and similarity networks (see Figure 2). Affiliation networks describe the membership of bibliographic entities, while similarity networks express similarities between bibliographic entities. Affiliation networks are represented by a weighted, directed graph whose nodes represent bibliographic entities of any type. Most common are bipartite affiliation networks, which depict a bipartite graph, i.e., there are only two types of nodes in the graph, and nodes of the same type must not be directly connected. A bipartite graph can be represented by a matrix \(A\) of size \(m\times n\), with \(m\) denoting the number of nodes of type one and \(n\) denoting the number of nodes of type two. The entry \(a_{ij}\) of \(A\) yields the value of the affiliation from the \(i^{th}\) node of type one to the \(j^{th}\) node of type two. Bipartite affiliation networks are named after their entity types, e.g., in an author-publication network, the nodes either depict an author or a publication, while the edges represent an affiliation from an author to a publication or vice versa. An intuitive example of such an affiliation is an edge in the graph from an author to a publication if the author has written the publication. [PERSON]'s network of journal articles can be considered a special type of affiliation network with articles as the only entity type occurring in the network. In contrast, similarity networks are _weighted_, _undirected graphs_. Every node of the graph represents an entity of the same type, e.g., all nodes represent authors. The nodes are connected by weighted, undirected edges, depicting the similarity between the connected nodes. These similarities are calculated by using a similarity measure expressing the similarity of two bibliographic entities. A similarity network is represented by its similarity matrix \(S\), being the graphs' adjacency matrix of size \(m\times m\), with \(m\) depicting the number of nodes of the graph. Each entry \(s_{ij}\) of \(S\) describes the similarity between node \(i\) and node \(j\). As adjacency matrices are quadratic, the graph of a similarity network is undirected, and \(S\) is symmetric. Dependent on the bibliographic entity type, different similarity measures can be used. An example of a similarity measure for authors is _co-authorship_. The co-authorship between two authors is defined by the number of academic publications they have published together. In order to measure the similarity of publications, _co-citation_ and _bibliographic coupling_ are commonly used, as well as some lexical measures. Figure 2: Bibliometric networks—overview. A co-citation of two publications is given if both publications are cited by a third publication, while two publications are bibliographically coupled if one or more citations of them are similar [1].