Network Robustness: Diffusing Information Despite Adversaries
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In this thesis, we consider the problem of diffusing information resiliently in networks that contain misbehaving nodes. Previous strategies to achieve resilient information diffusion typically require the normal nodes to hold some global information, such as the topology of the network and the identities of non-neighboring nodes. However, these assumptions are not suitable for large-scale networks and this necessitates our study of resilient algorithms based on only local information. We propose a consensus algorithm where, at each time-step, each normal node removes the extreme values in its neighborhood and updates its value as a weighted average of its own value and the remaining values. We show that traditional topological metrics (such as connectivity of the network) fail to capture such dynamics. Thus, we introduce a topological property termed as network robustness and show that this concept, together with its variants, is the key property to characterize the behavior of a class of resilient algorithms that use purely local information. We then investigate the robustness properties of complex networks. Specifically, we consider common random graph models for complex networks, including the preferential attachment model, the Erdos-Renyi model, and the geometric random graph model, and compare the metrics of connectivity and robustness in these models. While connectivity and robustness are greatly different in general (i.e., there exist graphs which are highly connected but with poor robustness), we show that the notions of robustness and connectivity are equivalent in the preferential attachment model, cannot be very different in the geometric random graph model, and share the same threshold functions in the Erdos-Renyi model, which gives us more insight about the structure of complex networks. Finally, we provide a construction method for robust graphs.