# MAT-61906 Complex Networks, 5 cr

#### Additional information

Suitable for postgraduate studies.

#### Person responsible

Kestutis Baltakys, Juho Kanniainen

#### Lessons

Implementation | Period | Person responsible | Requirements |

MAT-61906 2019-01 | 3 - 4 |
Kestutis Baltakys Juho Kanniainen |
Exam and project work |

#### Learning Outcomes

Complex network methods have become an important part of data science. They are applicable in many areas, including internet and WWW, social networks, transportation networks, biological networks, and financial networks, among others, whenever the system can be formally characterized by entities (nodes) and their interconnections (links). In fact, networks surround our daily lives, starting from the way people are connected through real and online friendships to the way airline companies connect the world via their flight routes. By using network techniques, one can better understand and predict the behavior of various complex systems. This truly interdisciplinary course introduces students to basic concepts and problems in complex networks with applications to various real-world situations. Students will be introduced to current research done in the field and at the end of the course will be able to apply their knowledge in practice. This course requires basic familiarity programming and matrix algebra. After completing the course, the student - knows key complex network definitions and measures - knows what kind of problems can be addressed using network methods - is familiar with most common network models - can do statistical network analysis - can construct networks using various network inference methods - can do a project starting with data analysis, network construction and analysis of network properties

#### Content

Content |
Core content |
Complementary knowledge |
Specialist knowledge |

1. |
Network representation: Adjacency matrix, un-/directed networks, un-/weighted networks, bipartite networks, trees, filtered networks, network components, multilayer network representations, network inference | ||

2. |
Network measures: node degrees, network density, number of paths of length n, Eigenvector/Katz/PageRank/Closeness Nentralities, cliques, clustering, homophily, assortative mixing | ||

3. |
Network structures: Degree distributions, small-world effect, power law and scale free networks, clusters and communities, motifs | ||

4. |
Network models: Random graphs, preferential attachment, exponential random graphs, epidemic models |

#### Instructions for students on how to achieve the learning outcomes

The grade of the course is based on the final exam and project work.

#### Assessment scale:

Numerical evaluation scale (0-5)

#### Partial passing:

#### Study material

Type |
Name |
Author |
ISBN |
URL |
Additional information |
Examination material |

Book | Networks: An Introduction | Mark Newman | ISBN-13: 9780199206650 | The course follows the selected chapters of the book. | No |

#### Prerequisites

Course | Mandatory/Advisable | Description |

MAT-01200 Insinöörimatematiikka X 2 | Mandatory | 1 |

MAT-01210 Insinöörimatematiikka A 2 | Mandatory | 1 |

MAT-01220 Insinöörimatematiikka B 2 | Mandatory | 1 |

MAT-01230 Insinöörimatematiikka C 2 | Mandatory | 1 |

MAT-01260 Matematiikka 2 | Mandatory | 1 |

MAT-01266 Mathematics 2 | Mandatory | 1 |

TIE-02107 Programming 1: Introduction | Mandatory | 1 |

MAT-01500 Insinöörimatematiikka X 5 | Advisable | 2 |

MAT-01510 Insinöörimatematiikka A 5 | Advisable | 2 |

MAT-01520 Insinöörimatematiikka B 5 | Advisable | 2 |

MAT-01530 Insinöörimatematiikka C 5 | Advisable | 2 |

MAT-01560 Matematiikka 5 | Advisable | 2 |

MAT-01566 Mathematics 5 | Advisable | 2 |

MAT-02500 Todennäköisyyslaskenta | Advisable | 2 |

MAT-02506 Probability Calculus | Advisable | 2 |

1 . Mutually alternative courses about matrix algebra

2 . Courses on statistics and probability theory

**Additional information about prerequisites**

Sufficient knowledge about matrix algebra and programming skills (python) are required. Knowledge on probability theory and statistics is strongly recommended. Correesponding courses on programmin and matrix algebra provided by other campuses are also eligible as prerequisites.

#### Correspondence of content

There is no equivalence with any other courses