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CHAPTER 10

Networks

Networks can be seen as abstractions of complex systems of interacting
entities (Newman, 2010). Network analysis is a scientific method based
on links and nodes as fundamental units. It originates from Euler’s famous
example in graph theory about the seven bridges of Ko ¨nigsberg (nowa-
days Kaliningrad). Ko ¨nigsberg is crossed by the river Pregel and had seven
bridges connecting both sides and two islands. Leonhard Euler was the
first to prove that it is not possible to take a walk through the city and
cross each bridge exactly once. In order to prove this, he abstracted the
problem to what is nowadays called a graph. Important applications in
informetrics are networks of collaborating authors, citing journals and
related entities showing the organization of science.

10.1 BASIC NETWORK THEORY
10.1.1 Definitions and Representations
A network or graph, G, is a pair of two related sets: G 5 (V,E) consisting
of a set V of vertices or nodes (used as synonyms) and a set E of edges,
links or arcs (also used as synonyms). Edges are ordered pairs of nodes,
representing a connection between these two nodes. We will use the
terms network and graph interchangeably. In sociological research nodes
are often referred to as actors.If W is a subset of V and if F is a subset of
E, then G s 5 (W,F) is a subgraph of G. Of course, each of the edges in F
must connect nodes that belong to W. Although they are theoretically
subgraphs of G 5 (V,E), the cases (Ø,Ø) and G 5 (V,E) will not be con-
sidered when talking about subgraphs of G.
Networks can be represented in different ways, including the follow-
ing three, (see Chapter 3: Publishing in Scientific Journals, where we
introduced these methods in the context of citation networks).
1. Two-dimensional graphs. By this we mean a two-dimensional
figure consisting of dots, representing nodes, and lines connecting
dots, representing the links. When lines intersect, this has no graph-
theoretical meaning in the sense that the intersection is not a new
node.

Becoming Metric-Wise © 2018 Elsevier Ltd.
DOI: http://dx.doi.org/10.1016/B978-0-08-102474-4.00010-8 All rights reserved. 315