Network analysis of dendritic fields not only defines the topology and connectivity of segments of an arborescence, but offers a means of discovering how networks grow. An important theory has recently been formulated29 suggesting that dendritic branching patterns may be established by synaptogenic interaction of dendritic growth cones with growing axons. This thesis may be verified through network analysis since the theory predicts that growth at pendant vertices will predominate in dendritic networks, that dendritic growth will be directed into areas of maximal synaptogenic activity and that arc lengths will be inversely related, and the order of branching at vertices directly related, to the magnitude of the synaptogenic activity operating about growing dendritic terminals. The possibility of a preponderance of terminal growth may be detected by comparing the topologies in an observed dendritic network with those of a series of hypothetical growth models. This paper provides the frequency table for models grown by monochotomous, dichotomous and trichotomous branching on random pendant vertices and random arcs for large networks in which 'set theory' contingencies are included. The paper also describes a method of calculating branching probabilities from the measurement of segment lengths, which is a means of testing the last mentioned prediction of the synaptogenic theory of denddritic growth. The method of network analysis is then discussed in relation to probable dendritic growth patterns, the constancy of segment lengths and the interaction of extrinsic and intrinsic factors in determining branching probabilities.