Three Essays on Triadic Evolution in a Large-scale Mobile Phone Network

This dissertation consists of three independent but related essays that explore different aspects of triadic evolution in a large-scale mobile phone network. The first essay tries to examine the randomness and robustness of the triangle decay and formation processes. By comparing the real and simulated transitional patterns, strong triadic preservation effect is detected and embeddedness in triangles keeps the node(s) and edge(s) from decaying. Even-higher-level comparisons are also made and I find that the square and pentagon decay over time by a stochastic random process. However, all the configuration formation processes at triadic, tetradic, and pentadic levels are not formed by chance. They come into being according to a systematic process in the real network.

Since we have known that the triangle decay and formation are not following a random process, the second essay analyzes the factors that could explain both triangle formation and persistence. Based on the logistic regression models, I find that most influencing factors at multiple levels have the same effects on the triangle survival and formation from structural holes processes. I also review various theories of triangle formation and persistence – balance theory, predisposition theory, tie strength theory, status homophily theory and embeddedness theory – and assess the extent to which reported findings are consistent with these theories.

Real social networks are often compared to random graphs in order to assess whether their typological structure could be the result of random processes. However, an Erdős-RŽnyi random graph in large scale is often lack of local structure beyond the dyadic level and as a result we need to generate the clustered random graph instead of the simple random graph to compare the local structure at the triadic level. In the third essay a generalized version of Gleeson's algorithm is advanced to generate a clustered random graph in large-scale which persists the number of nodes |V|, the number of edges |E|, and the global clustering coefficient as in the real network. And it also has advantages in randomness evaluation and computation time.