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## University of Groningen

Skip to 0 minutes and 10 seconds Complex systems are interacting elements, particles, units, individuals also responding to their environment without full central control. They can often be seen and depicted as networks. The branch of mathematics to describe and analyse networks is called graph theory. In graph theory, a network, or graph as it is called, is described as a set of nodes with links between the nodes, which are also called edges. The edges can be uni-directional, going in one direction, or bi-directional, going in both directions, or without a particular direction.

Skip to 1 minute and 0 seconds An edge means that the relation exists between the nodes. In social economic networks the nodes are people. Firms, government, banks, or any other organisation in which people participate. A network can, for example, describe a group of people showing who is friends with whom. There is an edge if there’s a friendship between two people. Complex systems are large, sometimes very large, networks. See, for example, the internet and Twitter. The nodes maybe different types of entities. For example, people on the one hand and jobs on the other hand. Such a graph is called bi-partied. This type of graph can be used to show the so-called matching problems, or markets. Let’s take an example. Let’s take a graph depicting matching problems of jobs.

Skip to 2 minutes and 5 seconds So on the one hand, we have a number of people looking for a job. And on the other hand, we have potential jobs. And a graph connects certain people to certain jobs. And what you can analyse if whether you can match the people with the jobs.

Skip to 2 minutes and 24 seconds So that’s a matching structure. If you look at social networks and look at their structure, we will immediately see that that structure is not constant over time. Social networks evolve. They are dynamic. To describe them evolutionary dynamics is an important tool. This will be discussed and described more extensively later in this course.

Skip to 2 minutes and 52 seconds Growth and development of social networks is historically important. That means that adding and deleting those nodes and edges is an element in their development. There’s much underlying dynamism in social networks. People die. Firms enter. Firms go bankrupt. People are born. New products appear. Products disappear.

Skip to 3 minutes and 24 seconds Edges may pass on something from node to node, like information, knowledge, money, value. All these things may travel through the edges. Think again about the social media. Through the social media a lot of information is travelling between different people, different nodes, in the network. Take the example of market transaction as a bidirectional graph in which money and goods travel between them at the edges. Money from one person to the other and goods in the other direction in a market transaction. In this lecture we have shown that complex systems can often be seen and depicted as networks. And we have discussed some basics of graph theory. That’s the branch of mathematics dealing with networks.

# Introduction to networks

This lecture introduces a new way to look at complex systems, namely, as a network.

In Graph Theory you can look at networks as sets of nodes that are connected by edges. These connections can be either unidirectional, bidirectional or without direction.