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The Ohio State University

1. Fernandez Puentes, Isabel C. Stability of Degree Distributions and Analysis of Community Structures in Social Networks.

Degree: PhD, Electrical and Computer Engineering, 2019, The Ohio State University

Recent efforts in network theory aim to characterize the structures of empirical social networks. Power-law degree distributions and highly interconnected communities are commonly observed properties in social networks. Our work focuses on closing the gap between control and network theory by introducing an unified framework that explains the emergence of these two properties from preferential attachment and assortativity mechanisms. First, we center our attention on showing that the dynamics of the complementary cumulative degree distributions can be represented as infinite dimensional time-varying linear systems. In particular, we extend the class of preferential attachment models by considering scenarios in which the number of new connections may vary as more nodes join the network. Second, we show that the models have stable invariants that capture the limit distributions of the degree of nodes. In other words, under small perturbations of initial conditions, the evolution of the degree distributions remains close to the invariant at any point in time. Finally, for networks with assortative mixing in terms of node type (homophilic relationships), we characterize the division of the network into communities. Specifically, we prove the convergence of homophily, measured at the group level and network level, and community modularity. Advisors/Committee Members: Passino, KEvin (Advisor).

Subjects/Keywords: Mathematics; Systems Science; Electrical Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Fernandez Puentes, I. C. (2019). Stability of Degree Distributions and Analysis of Community Structures in Social Networks. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1545317072963346

Chicago Manual of Style (16th Edition):

Fernandez Puentes, Isabel C. “Stability of Degree Distributions and Analysis of Community Structures in Social Networks.” 2019. Doctoral Dissertation, The Ohio State University. Accessed October 23, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1545317072963346.

MLA Handbook (7th Edition):

Fernandez Puentes, Isabel C. “Stability of Degree Distributions and Analysis of Community Structures in Social Networks.” 2019. Web. 23 Oct 2019.

Vancouver:

Fernandez Puentes IC. Stability of Degree Distributions and Analysis of Community Structures in Social Networks. [Internet] [Doctoral dissertation]. The Ohio State University; 2019. [cited 2019 Oct 23]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1545317072963346.

Council of Science Editors:

Fernandez Puentes IC. Stability of Degree Distributions and Analysis of Community Structures in Social Networks. [Doctoral Dissertation]. The Ohio State University; 2019. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1545317072963346

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