Date of Award

12-2020

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computer Engineering and Sciences

First Advisor

Marco M. Carvalho

Second Advisor

Adrian Peter

Third Advisor

William H. Allen

Fourth Advisor

Philip J. Bernhard

Abstract

From social to biological networks, prior research in complex networks have demonstrated the importance of the frequency and distribution of different types of motifs to important network functions and properties. A network motif (or graphlet) is defined as a small connected sub-pattern which is over-represented in a network. Network motifs have been widely applied in a wide range of applications, namely biological, social, and technical networks. The counting of the network motif involves expensive enumeration of graph sub-patterns along with the detection of graph isomorphism. In general, network motif detection algorithms are computationally expensive and often designed to operate over static networks, which is infeasible for dynamic network structures. While significant work has been conducted to improve the efficiency of motif enumeration algorithms for complex networks, it is generally accepted that for most applications where dynamic net-work structure is important, the use of such algorithms is very limited and often impractical. In this dissertation, we emphasize on providing an exact count of a selected set of motifs in dynamic networks. We propose, develop, and demonstrate an efficient and robust algorithmic approach to achieve fast enumeration of motif distribution based on localized changes in network structure. The proposed technique will enable the tracking of motif distributions in large scale dynamic networks. We show how our algorithm can quickly update the frequency of different network motifs in dynamic networks. Starting from an initial frequency of network motif types, the proposed algorithmic approach monitors local network changes. Then, it efficiently updates the motif distribution at run-time without requiring the re-evaluation of the complete network, thereby avoiding redundant searches. The experimental results show that our approach is successful in reducing the computational time by eliminating the overlapped sub-patterns. Run-time monitoring of network motif distributions is very important in numerous practical domains where large networks are subject to localized changes.

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