## Visual analytics for large- scale actor networks: a case study of Liverpool, 1750–1810

Figure 6.1 Possible visualisations using VA (source: Haggerty and Haggerty, 2012).

The adjacency matrix forms the basis of a graph. A graph (G) comprises a set of vertices (or points, V) (the actors) which are connected to other points through edges (or arcs, E) (the relationships between the actors); or G = (V, E). V and E are taken to be finite and a vertex can exist within a graph and not have any associated edges, i.e. they are unconnected to other vertices. Two vertices that are directly connected by an edge are said to be adjacent. The number of other vertices to which any given vertex is adjacent is called the degree of that point. The distance between vertices is calculated by the number of edges in a path. The shortest paths linking pairs of vertices (as there may be many paths linking vertex pairs (actors) within a network) are called geodesics. Vertices falling on the geodesics between a given pair of vertices stand between these points. The order of a graph is the number of vertices while its size is expressed as the number of edges. Conceptualising networks in this way enables us to visualise, quantify and measure relationships between actors as well as the network institution, as will be demonstrated in our case study. A simple graph, based on Table 6.1, is shown in Figure 6.2, in which Points 1 to 5 represent the actors.