#### Abstract

It is increasingly common to find real-life structures or behaviors represented as graphs in many areas of the computing sciences. Comparing these graphs is a hard task, especially when we are interested in assigning a non-binary similarity score between two large graphs based on some domain-specific context. In bioinformatics, social network analysis and other areas is frequently necessary to compute graph similarities based on the local topological information of each vertex of the given graphs. This is why graphlet degree vectors have become more and more popular in these areas. They provide a simple yet detailed representation of a vertex's topology by counting the number of times such vertex touches a list of small predefined sub-structures called graphlets. In this thesis, we study the state-of-the-art algorithm to compute graphlet degree vectors, the Orbit Counting Algorithm (ORCA). ORCA generates a triangular system of linear equations that can be quickly solved to obtain the graphlet degree vector of a vertex. We make theoretical and practical improvements to this algorithm and measure the difference in speed after these improvements. The theoretical improvement consists of finding automorphisms of graphlets given a fixed vertex that is required to map to itself in such automorphisms. We observe that one piece of the algorithm runs much faster than before with this improvement, especially for larger graphlet orders. This helps the algorithm take less time in generating the linear system that we use to find the desired graphlet degree vector. The practical improvement consists of making a flexible implementation of the algorithm, which can take any graphlet size as input, any number of input graphs, and compute the graphlet degree vector for every vertex in each one of those graphs.

#### Library of Congress Subject Headings

Graph theory--Data processing; Algorithms

#### Publication Date

8-22-2018

#### Document Type

Thesis

#### Student Type

Graduate

#### Degree Name

Applied and Computational Mathematics (MS)

#### Department, Program, or Center

School of Mathematical Sciences (COS)

#### Advisor

Carlos R. Rivero

#### Advisor/Committee Member

Darren Narayan

#### Advisor/Committee Member

Jobby Jacob

#### Recommended Citation

Nunez, Wilberto Z., "Improvements on ORCA for Fast Computation of Graphlet Degree Vectors of any Graphlet Order" (2018). Thesis. Rochester Institute of Technology. Accessed from

https://scholarworks.rit.edu/theses/9892

#### Campus

RIT – Main Campus

#### Plan Codes

ACMTH-MS