Abstract

Influence has been studied across many different domains including sociology, statistics, marketing, network theory, psychology, social media, politics, and web search. In each of these domains, being able to measure and rank various degrees of influence has useful applications. For example, measuring influence in web search allows internet users to discover useful content more quickly. However, many of these algorithms measure influence across networks and graphs that are mathematically static. This project explores influence measurement within the context of linear time invariant (LTI) systems. While dynamical networks do have mathematical models for quantifying influence on a node-to-node basis, to the best of our knowledge, there are no proposed mathematical formulations that measure aggregate level influence across an entire dynamical network. The dynamics associated with each link, which can differ from one link to another, add additional complexity to the problem. Because of this complexity, many of the static-graph approaches used in web search do not achieve the desired outcome for dynamical networks. In this work we build upon concepts from PageRank and systems theory introduce two new methods for measuring influence within dynamical networks: 1) Dynamical Responsive Page Rank (DRPR) and 2) Aggregated Targeted Reachability (ATR). We then compare and analyze and compare results with these new methods.

Degree

College and Department

Physical and Mathematical Sciences; Computer Science

Rights

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