Reconstructing a Graph from Path Traces
This addresses a network reconstruction problem for applications like social or biological networks, but it is incremental as it builds on existing trace-based methods with specific theoretical analyses.
The paper tackles the problem of inferring a network's structure from unordered path traces by proposing an algorithm that orders traces based on node co-occurrence frequencies, and it derives exact recovery conditions for 3-node traces and error probabilities for random graphs.
This paper considers the problem of inferring the structure of a network from indirect observations. Each observation (a "trace") is the unordered set of nodes which are activated along a path through the network. Since a trace does not convey information about the order of nodes within the path, there are many feasible orders for each trace observed, and thus the problem of inferring the network from traces is, in general, illposed. We propose and analyze an algorithm which inserts edges by ordering each trace into a path according to which pairs of nodes in the path co-occur most frequently in the observations. When all traces involve exactly 3 nodes, we derive necessary and sufficient conditions for the reconstruction algorithm to exactly recover the graph. Finally, for a family of random graphs, we present expressions for reconstruction error probabilities (false discoveries and missed detections).