It is beyond the scope of this appendix to expound a fully fledged graph theory. The purpose of the appendix is to give a description of graph theory at a level which provides non-mathematicians with a working knowledge to analyze the main properties of social networks.
Graph theory is the study of graphs, mathematical structures, used to model pairwise relations between entities. It is visually made of vertices or nodes connected by edges. These relations can be directed or undirected. Directed relations mean that the interaction is one-way between the influencer and the influenced. Relations can be bidirectional, meaning that the influence between the two actors is reciprocal.
There are two alternative formalisms which yield representations either by a diagram of nodes and edges or by a matrix that codes the ties between pairs of nodes. They contain the same information and thus any one can be derived from another. Each representation has some advantages. A diagram delivers an immediate visual understanding of the network structure, whereas the matrix representation is better suited to carry out quantitative manipulations of network properties.
Three illustrative networks are shown in Figure A1.1 in both formalisms.
In the matrix ...