The Marginal Benefit of Monitor Placement on Networks

4 Inferring the structure of an unknown network is a difficult problem of interest to researchers, academics, and industry. We develop a novel algorithm to infer nodes and edges in an unknown network. Our algorithm 6 utilizes sensors that have the capability to detect adjacent nodes and their labels, as well as and incident edges to the monitor. The algorithm places new sensors at the highest degree neighboring node that has 8 been inferred, and it will restart when attempting to place a sensor at a node where a sensor already exists. The algorithm has an adjustable restarting feature which varies between restarting at a previously discovered 10 but unmonitored node and a random teleportation to an unexplored node somewhere in the network. We compare the inference performance of our algorithm against inference through random walks and random 12 placement in four distinct network a Barabási-Albert network, an Erdős-Rényi random network, and two data sets from the Stanford Large Network Dataset Collection [11]. Our algorithm outperforms random 14 walk inference and random placement of monitors type of inference in edge discovery in all test cases. Our algorithm outperforms them in node inference in the synthetic data; in real data it outperforms them in the 16 beginning of the inference and we explain why. A website was created where these algorithms can be tested live on preloaded networks or custom networks as desired by the user. The visualization also displays the 18 network as it is being inferred, and it provides other statistics about the real and inferred network. network topology, distance between graphs (similarity), graph comparison metrics, distance in a graph. 2