### 2017　Complex Networks

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Academic unit or major
Graduate major in Artificial Intelligence
Instructor(s)
Takayasu Misako  Murata Tsuyoshi  Ishii Hideaki
Course component(s)
Lecture
Day/Period(Room No.)
Mon3-4(G115,W833)  Thr3-4(G115,W833)
Group
-
Course number
ART.T462
Credits
2
Academic year
2017
Offered quarter
4Q
Syllabus updated
2017/3/17
Lecture notes updated
2018/1/29
Language used
English
Access Index

### Course description and aims

This course is for the abilities of understanding and analyzing network structures of
complex systems. We study from the viewpoints of network metrics, algorithms, models and
processes.

This course aims at the following three.
1) Study of basic concepts of network structures
2) Practice of network analysis with tools
3) Understand examples of applications of complex networks in various fields

### Student learning outcomes

The goal of this course is to obtain the following abilities.
1) Understanding basic metrics of network structures and computing them for given networks
2) Understanding basic algorithms of network structures
3) Understanding models for network generation and simulating simple ones
4) Understanding the processes on networks such as epidemics

### Keywords

Complex networks, Graph theory, Mathematical models

### Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- - -

### Class flow

The first half will be given in a lecture style based on slides and other course material on an overview of complex networks and their analysis. The second half will be given by specialists in different areas to present application examples where complex network methods have significant impacts. The topics include (but not limited to) biological systems, gene networks, synchronization phenomena, networks of webpages, social/economic networks, and electrical power systems.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction, history of the development of graph theory and network science, tools for network analysis Report assignment (given during the lecture)
Class 2 Metrics of networks (1) (adjacency matrix, tree, planar network, degree, path, component, connectivity) Report assignment (given during the lecture)
Class 3 Metrics of networks (2) (graph Laplacian, random walk, degree centrality, eigenvector centrality, closeness centrality, betweenness centrality) Report assignment (given during the lecture)
Class 4 Algorithms (1) (shortest path, Dijkstra's algorithm, maximum flow algorithm) Report assignment (given during the lecture)
Class 5 Algorithms (2) (graph partition, community detection) Report assignment (given during the lecture)
Class 6 Models (random graph, power-law distribution, scale free, small-world) Report assignment (given during the lecture)
Class 7 Processes (epidemics, SI model, SIR model) Report assignment (given during the lecture)
Class 8 Application of complex networks 1: Social networks (1) Report assignment (given during the lecture)
Class 9 Application of complex networks 2: Social networks (2) Report assignment (given during the lecture)
Class 10 Application of complex networks 3：Networks in biological systems (1) Report assignment (given during the lecture)
Class 11 Application of complex networks 4: Networks in biological systems (2) Report assignment (given during the lecture)
Class 12 Application of complex networks 5: Control of networked agent systems (1) Report assignment (given during the lecture)
Class 13 Application of complex networks 6: Control of networked agent systems (2) Report assignment (given during the lecture)
Class 14 Current research in complex networks 1: Routing in networks Report assignment (given during the lecture)
Class 15 Current research in complex networks 2: Analysis of networks of companies Report assignment (given during the lecture)

### Textbook(s)

１． Networks: An Introduction, M. E. J. Newman, Oxford University Press

### Reference books, course materials, etc.

１． Networks: An Introduction, M. E. J. Newman, Oxford University Press

### Assessment criteria and methods

Reports and exams (the dates will be announced during the lectures)

### Related courses

• ART.T455 ： Modeling of Discrete Systems
• ART.T451 ： Mathematics of Discrete Systems

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Linear algebra and calculus at the undergraduate level is required for taking this course.