Pawel Pralat

This book concentrates on mining networks, a subfield within data science. Many data science problems can be viewed as a study of some properties of complex networks in which nodes represent the entities that are being investigated, and edges represent relations between these entities. In these networks (for example, Instagram and Facebook online social networks), nodes not only contain some useful information (such as the user’s profile, photos, tags) but are also internally connected to other nodes (relations based on follower requests, similar users’ behavior, age, geographic location). Such networks are often large-scale, decentralized, and evolve dynamically over time. Mining complex networks to understand the principles governing the organization and the behavior of such networks is crucial for a broad range of fields of study, including information and social sciences, economics, biology, and neuroscience. The field has seen significant advancements since the first edition was published. Changes and updates to this edition include: New material and examples on random geometric graphs The chapter on node embeddings was augmented in several places including a discussion on classical vs. structural embeddings, more details on graph neural networks (GNNs), as well as other directions. Several new tools and techniques are introduced on mining hypergraphs New material on post-processing for overlapping communities A new focus on a framework for embedding graphs codeveloped by the authors. A short chapter on fairness in network mining models. This book is aimed at being suitable for an upper-year undergraduate course or a graduate course.

This book concentrates on mining networks, a subfield within data science. Many data science problems can be viewed as a study of some properties of complex networks in which nodes represent the entities that are being investigated, and edges represent relations between these entities. In these networks (for example, Instagram and Facebook online social networks), nodes not only contain some useful information (such as the user’s profile, photos, tags) but are also internally connected to other nodes (relations based on follower requests, similar users’ behavior, age, geographic location). Such networks are often large-scale, decentralized, and evolve dynamically over time. Mining complex networks to understand the principles governing the organization and the behavior of such networks is crucial for a broad range of fields of study, including information and social sciences, economics, biology, and neuroscience. The field has seen significant advancements since the first edition was published. Changes and updates to this edition include: New material and examples on random geometric graphs The chapter on node embeddings was augmented in several places including a discussion on classical vs. structural embeddings, more details on graph neural networks (GNNs), as well as other directions. Several new tools and techniques are introduced on mining hypergraphs New material on post-processing for overlapping communities A new focus on a framework for embedding graphs codeveloped by the authors. A short chapter on fairness in network mining models. This book is aimed at being suitable for an upper-year undergraduate course or a graduate course.

This book concentrates on mining networks, a subfield within data science. Data science uses scientific and computational tools to extract valuable knowledge from large data sets. Once data is processed and cleaned, it is analyzed and presented to support decision-making processes. Data science and machine learning tools have become widely used in companies of all sizes. Networks are often large-scale, decentralized, and evolve dynamically over time. Mining complex networks aim to understand the principles governing the organization and the behavior of such networks is crucial for a broad range of fields of study. Here are a few selected typical applications of mining networks: Community detection (which users on some social media platforms are close friends). Link prediction (who is likely to connect to whom on such platforms). Node attribute prediction (what advertisement should be shown to a given user of a particular platform to match their interests). Influential node detection (which social media users would be the best ambassadors of a specific product).This textbook is suitable for an upper-year undergraduate course or a graduate course in programs such as data science, mathematics, computer science, business, engineering, physics, statistics, and social science. This book can be successfully used by all enthusiasts of data science at various levels of sophistication to expand their knowledge or consider changing their career path. Jupiter notebooks (in Python and Julia) accompany the book and can be accessed on https://www.ryerson.ca/mining-complex-networks/. These not only contain all the experiments presented in the book, but also include additional material. Bogumil Kaminski is the Chairman of the Scientific Council for the Discipline of Economics and Finance at SGH Warsaw School of Economics. He is also an Adjunct Professor at the Data Science Laboratory at Ryerson University. Bogumil is an expert in applications of mathematical modeling to solving complex real-life problems. He is also a substantial open-source contributor to the development of the Julia language and its package ecosystem.Pawel Pralat is a Professor of Mathematics in Ryerson University, whose main research interests are in random graph theory, especially in modeling and mining complex networks. He is the Director of Fields-CQAM Lab on Computational Methods in Industrial Mathematics in The Fields Institute for Research in Mathematical Sciences and has pursued collaborations with various industry partners as well as the Government of Canada. He has written over 170 papers and three books with 130 plus collaborators.François Théberge holds a B.Sc. degree in applied mathematics from the University of Ottawa, a M.Sc. in telecommunications from INRS and a PhD in electrical engineering from McGill University. He has been employed by the Government of Canada since 1996 where he was involved in the creation of the data science team as well as the research group now known as the Tutte Institute for Mathematics and Computing. He also holds an adjunct professorial position in the Department of Mathematics and Statistics at the University of Ottawa. His current interests include relational-data mining and deep learning.

This book provides a broad overview of the state of the art of the research in generative methods for the analysis of social media data. It especially includes two important aspects that currently gain importance in mining and modelling social media: dynamics and networks. The book is divided into five chapters and provides an extensive bibliography consisting of more than 250 papers. After a quick introduction and survey of the book in the first chapter, chapter 2 is devoted to the discussion of data models and ontologies for social network analysis. Next, chapter 3 deals with text generation and generative text models and the dangers they pose to social media and society at large. Chapter 4 then focuses on topic modelling and sentiment analysis in the context of social networks. Finally, Chapter 5 presents graph theory tools and approaches to mine and model social networks. Throughout the book, open problems, highlighting potential future directions, are clearly identified. The book aims at researchers and graduate students in social media analysis, information retrieval, and machine learning applications.

Graph Searching Games and Probabilistic Methods is the first book that focuses on the intersection of graph searching games and probabilistic methods. The book explores various applications of these powerful mathematical tools to games and processes such as Cops and Robbers, Zombie and Survivors, and Firefighting. Written in an engaging style, the book is accessible to a wide audience including mathematicians and computer scientists. Readers will find that the book provides state-of-the-art results, techniques, and directions in graph searching games, especially from the point of view of probabilistic methods. The authors describe three directions while providing numerous examples, which include: • Playing a deterministic game on a random board. • Players making random moves. • Probabilistic methods used to analyze a deterministic game.

This book concentrates on mining networks, a subfield within data science. Data science uses scientific and computational tools to extract valuable knowledge from large data sets. Once data is processed and cleaned, it is analyzed and presented to support decision-making processes. Data science and machine learning tools have become widely used in companies of all sizes. Networks are often large-scale, decentralized, and evolve dynamically over time. Mining complex networks aim to understand the principles governing the organization and the behavior of such networks is crucial for a broad range of fields of study. Here are a few selected typical applications of mining networks: Community detection (which users on some social media platforms are close friends). Link prediction (who is likely to connect to whom on such platforms). Node attribute prediction (what advertisement should be shown to a given user of a particular platform to match their interests). Influential node detection (which social media users would be the best ambassadors of a specific product).This textbook is suitable for an upper-year undergraduate course or a graduate course in programs such as data science, mathematics, computer science, business, engineering, physics, statistics, and social science. This book can be successfully used by all enthusiasts of data science at various levels of sophistication to expand their knowledge or consider changing their career path. Jupiter notebooks (in Python and Julia) accompany the book and can be accessed on https://www.ryerson.ca/mining-complex-networks/. These not only contain all the experiments presented in the book, but also include additional material. Bogumil Kaminski is the Chairman of the Scientific Council for the Discipline of Economics and Finance at SGH Warsaw School of Economics. He is also an Adjunct Professor at the Data Science Laboratory at Ryerson University. Bogumil is an expert in applications of mathematical modeling to solving complex real-life problems. He is also a substantial open-source contributor to the development of the Julia language and its package ecosystem.Pawel Pralat is a Professor of Mathematics in Ryerson University, whose main research interests are in random graph theory, especially in modeling and mining complex networks. He is the Director of Fields-CQAM Lab on Computational Methods in Industrial Mathematics in The Fields Institute for Research in Mathematical Sciences and has pursued collaborations with various industry partners as well as the Government of Canada. He has written over 170 papers and three books with 130 plus collaborators.François Théberge holds a B.Sc. degree in applied mathematics from the University of Ottawa, a M.Sc. in telecommunications from INRS and a PhD in electrical engineering from McGill University. He has been employed by the Government of Canada since 1996 where he was involved in the creation of the data science team as well as the research group now known as the Tutte Institute for Mathematics and Computing. He also holds an adjunct professorial position in the Department of Mathematics and Statistics at the University of Ottawa. His current interests include relational-data mining and deep learning.

This accessible book helps readers to see the bigger picture of advanced mathematics. The book contains carefully selected, challenging problems in an easy-to-follow, step-by-step process. Neither prior preparation nor any mathematical sophistication is required. The authors guide the reader to “train their brain” to think and express themselves in a rigorous, mathematical way, and to extract facts, analyze the problem, and identify main challenges. A firm foundation in a diverse range of topics is presented. Moreover, the authors show how to draw appropriate, true conclusions. Computer support is used to better intuition into discussed problems. The book is designed for self-study. It can be used to bridge the gap between introductory calculus/linear algebra courses and more advanced courses offered at universities. It improves the ability to read, write, and think in a rigorous, mature mathematical fashion. The reader will develop a deeper understanding in preparation to succeed in more advanced course work. Features•The authors employ a six-step process: 1.SOURCE2.PROBLEM3.THEORY4.SOLUTION5.REMARK6.EXERCISES •An Appendix introduces programming in Julia This book is also suitable for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions.

This accessible book helps readers to see the bigger picture of advanced mathematics. The book contains carefully selected, challenging problems in an easy-to-follow, step-by-step process. Neither prior preparation nor any mathematical sophistication is required. The authors guide the reader to “train their brain” to think and express themselves in a rigorous, mathematical way, and to extract facts, analyze the problem, and identify main challenges. A firm foundation in a diverse range of topics is presented. Moreover, the authors show how to draw appropriate, true conclusions. Computer support is used to better intuition into discussed problems. The book is designed for self-study. It can be used to bridge the gap between introductory calculus/linear algebra courses and more advanced courses offered at universities. It improves the ability to read, write, and think in a rigorous, mature mathematical fashion. The reader will develop a deeper understanding in preparation to succeed in more advanced course work.Features•The authors employ a six-step process: 1.SOURCE2.PROBLEM3.THEORY4.SOLUTION5.REMARK6.EXERCISES•An Appendix introduces programming in JuliaThis book is also suitable for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions.

Graph Searching Games and Probabilistic Methods is the first book that focuses on the intersection of graph searching games and probabilistic methods. The book explores various applications of these powerful mathematical tools to games and processes such as Cops and Robbers, Zombie and Survivors, and Firefighting. Written in an engaging style, the book is accessible to a wide audience including mathematicians and computer scientists. Readers will find that the book provides state-of-the-art results, techniques, and directions in graph searching games, especially from the point of view of probabilistic methods. The authors describe three directions while providing numerous examples, which include: • Playing a deterministic game on a random board. • Players making random moves. • Probabilistic methods used to analyze a deterministic game.