Complex networks are everywhere in the world around us: communication networks, transportation networks, networks of friends and acquaintances, and biological networks, to name a few. In this course, students will learn the similarities and mathematical abstractions that lie beneath these examples. Other examples drawn from molecular biology (gene regulation and protein interaction networks), economics (trade networks, relationships between companies and the strategic interactions on networks), computer networks (Internet, world wide web), and ecology (food webs). In the last decade there has been an explosion of work in the theory and applications of networks to a vast range of problems. Students who complete this course will receive a broad introduction to recent work in this area, understand the strengths and weaknesses of modeling the network, and may apply networks and their analysis in a variety of configurations.
In the first part of the course we focus on the empirical description of the network structure. Then, we turn our attention to the dynamics of networks: how networks are formed and grow, and how these rules of growth are related to the overall structure. Finally, we consider algorithms and dynamics on top of networks. In the latter part of the course we will present issues related to the spread of diseases and viruses in the network, how to detect the community structure in networks, and for example, how it works the Google PageRank algorithm.
Person in charge
Sergio Gómez Jiménez (
Alexandre Arenas (
Generic Technical Competences
CG3 - Capacity for modeling, calculation, simulation, development and implementation in technology and company engineering centers, particularly in research, development and innovation in all areas related to Artificial Intelligence.
Technical Competences of each Specialization
CEA11 - Capability to understand the advanced techniques of Computational Intelligence, and to know how to design, implement and apply these techniques in the development of intelligent applications, services or systems.
CEP2 - Capability to solve the decision making problems from different organizations, integrating intelligent tools.
CT4 - Capacity for managing the acquisition, the structuring, analysis and visualization of data and information in the field of specialisation, and for critically assessing the results of this management.
CT6 - Capability to evaluate and analyze on a reasoned and critical way about situations, projects, proposals, reports and scientific-technical surveys. Capability to argue the reasons that explain or justify such situations, proposals, etc..
Analisis y sintesis
CT7 - Capability to analyze and solve complex technical problems.
CB6 - Ability to apply the acquired knowledge and capacity for solving problems in new or unknown environments within broader (or multidisciplinary) contexts related to their area of study.
Detection of systems which may be represented using complex networks
To know how to study and characterize the structure of complex networks
To know models of complex networks and their implementation
To know the main dynamics on top of complex networks
To know how to perform and validate Monte Carlo simulations
To know how to apply the knowledge in complex networks to extract information of systems which can be described using this framework
Examples of complex networks in many knowledge fields. Complex network types.
Structure of complex network
Main topological and structural characteristics of complex networks: degree distribution, small-world, clustering, assortativity, community structure, centrality, etc. Community detection algorithms.
Complex network models
Erdös-Renyi random networks, Barabasi-Albert model, Watts-Strogatz model, configurational model, etc.
Dynamics on complex networks
Most important dynamics on complex networks: epidemic spreading, synchronization, diffusion, evolutionary games, percolation, etc. Monte Carlo simulations. Phase transitions.