A network cascade is a process in which an effect spreads rapidly through a network, influencing the behavior or state of nodes, often in a self-reinforcing manner. The structure of the underlying network plays a crucial role in the cascade's evolution. For example, if a high-degree node is affected, it can propagate the cascade widely to its neighbors.

This project tackles the following question. Given multiple observations of cascades over the same unknown network, what can be inferred about the network itself?

Existing research often aims to reconstruct the entire network but typically requires observing a large number of cascades. Recent studies, however, have shown that it is possible to identify high-degree nodes with only a few cascade observations [1].

This project has two main objectives:

• To explore whether the method used in [1] can be extended to noisy cascade observations.
• To investigate if other network structures, such as the presence of communities, clustering coefficients, or degree assortativity, can be inferred from observing a limited number of cascades.

[1] Finding Super-spreaders in Network Cascades. Elchanan Mossel, Anirudh Sridhar; Proceedings of Thirty Seventh Conference on Learning Theory, PMLR 247:3874-3914