Date of Graduation
2019
Document Type
Thesis
Degree Type
MS
College
Eberly College of Arts and Sciences
Department
Mathematics
Committee Chair
Marjorie Darrah
Committee Member
Roxann Humbert
Committee Member
Jessica Deshler
Abstract
Social network analysis seeks to understand the structure of relationships in networks of actors. As researchers identify structural properties of interest (e.g. vulnerability to network cuts) they introduce measures to quantify the expression of those properties in observed networks. In fact, it is not uncommon that multiple measures are introduced purporting to evaluate a single property. Relative merits of competing measures are not self-evident but the corresponding inferences can conflict, encouraging arbitrary choice among measures and endangering the validity of conclusions. We argue (i) that multiplicity of measures is a necessary consequence of the de rigueur practice of conflating different facets of actor association as “tie strength,” and (ii) that distinguishing among distinct facets of tie strength, the primitive unit of Social Network data, implies choices among measures used for other properties. In particular, distinct types of association data (e.g. frequency of contact, emotional depth) must be given distinct mathematical treatment. Hence multiplicity of structural property measures can be reduced to and solved as a problem of multiplicity of treatments for ties. To this end we propose a general framework for evaluation of paths in terms of their ties and introduce novel measures of network connectedness in terms of ties. A key feature of one measure, which we call social conductivity or sconductivity, is its simultaneous accounting for all paths of connection between nodes, which we believe is novel. We discuss the relationship between dimensions of tie strength and appropriate choices from our path-evaluation framework, and show how these choices map bijectively with choices among measures of other structural properties. We conclude by demonstrating the application of the method to the analysis of a network dataset. The methods described have been implemented in an open source software package and published on the Comprehensive R Archive Network.
Recommended Citation
Buch, David Anthony, "Tie Strength, Optimal Connections, and Distance in Social Networks" (2019). Graduate Theses, Dissertations, and Problem Reports. 7400.
https://researchrepository.wvu.edu/etd/7400