In this paper, we consider topology identification of large-scale interconnected dynamical systems. The system topology under study has the structure of a directed graph. Each edge of the directed network graph represents a Finite Impulse Response (FIR) filter with a possible transport delay. Each node is a summer, whose inputs are the signals from the incoming edges, while the output of the summer is sent to outgoing edges. Edges of the graph can be of different unknown orders and delays. Both the graph topology and the FIR filters and delays that make up the edges are unknown. We aim to do the topology identification from the smallest possible number of node observations when there is limited data available and for this reason, we call this problem Compressive Topology Identification (CTI).