All networks are made up of vertices (points interconnected by segments), which include terminals interconnected by terminal segments, nodes interconnected by link segments and the root point connected to the tree by the root segment. All nodes may be classified into unique types according to the number of terminal and link segments they drain. For example, there are three distinct dichotomous nodes, a `primary' node draining two terminal segments, a `secondary' node draining one terminal segment and a link segment, and a `tertiary' node draining two link segments. The numbers of primary and tertiary nodes approximate to equality in large networks and thus the ratio of primary to secondary nodes defines topology. All higher order nodes (trichotomous and beyond) may be resolved into dichotomous forms and incorporated into the analysis. Different forms of growth may thus be analysed by comparing the frequency distributions of nodes with those generated by computer simulated growth models. Moreover, all vertices can be ordered so that metrical parameters are easily incorporated and the hierarchical arrangements of vertices of different order discerned. The dendritic trees of 48 Purkinje cells, taken from folia along the primary fissure, were analysed using vertex analysis. The mean number of segments in Purkinje cell trees was 881 $\pm $ 23 (s.e.) and mean total dendritic length 7959 $\pm $ 233 (s.e.) $\mu $m. Segment lengths were longest over proximal segments but over most of the tree segment lengths were constant at 10 $\pm $ 0.2 (s.e.) $\mu $m. Vertex, segment and terminal frequency distributions of equivalent orders were all normal with a slight positive skew. Peak frequencies were recorded at the 12th equivalent order. The mean primary/secondary nodal vertex ratio was 0.93 and the proportion of trichotomous branch points in the tree was 5%. Comparison of the frequency distribution of all vertices with computer generated models showed that growth of the Purkinje cell was most closely simulated by a random terminal growth model, incorporating 5% trichotomy, in which the branching of high order terminals was more likely than low order terminals. It was concluded that growth of the Purkinje cell tree could proceed by random terminal branching with growth occuring preferentially over a front composed of terminals that are ascending through a corridor in the molecular layer whose margins are defined by neighbouring trees.