# IMAGINARY, Masterclass and social networks

Mathematics exhibition "IMAGINARY: beauty and power of mathematics" is ready to reopen its doors in Eindhoven!

In February the exhibition will be in Eindhoven, from the 14th of February to the 2nd of March. It can be found in the Atlas building on the campus of the Eindhoven University of Technology.

The NETWORKS program will also be present at the exhibition in Eindhoven! The yearly two-day masterclass NETWORKS goes to school 2023, which will be organized in Eindhoven on the 28th of February and the 2nd of March will be part of the activities program. If you are a teacher and you want to join the masterclass with your students, have a look at the detailed program here, you can register directly here.

In the exhibition, you can also see four posters on networks and algorithms! These were made in collaboration with various people. One of these posters is about structure in social networks. This poster was made by Clara Stegehuis, assistant professor at Twente University.

The poster can be seen below. Below the poster in English, you can read more details about this modern line of research, which is also related to the talk of Martijn Gösgens at the masterclass!

### Communities in social networks

Before you can start looking for the network communities, we first have to know what a community is. The poster suggests that a community has the following properties:

- There exist relatively many connections between nodes in the same community.

- There exist relatively few connections between nodes in different communities.

To find the network communities, we need a mathematical equation that describes when a division of the network into communities meets these two criteria. One of the first such equations, the so-called modularity equation, uses exactly these two community properties.

Suppose we divide a network into several groups. Then the modularity of this network division is an equation with two terms. The first term counts the number of connections within all groups. In short, this says that we would like to have as many connections as possible within the groups. Unfortunately, only maximizing this term will not help.

If we only maximize the number of connections within the groups, then the best division is to put all nodes of the network into one large community. In that case, all network connections are within the same community. To overcome this problem, the modularity equation subtracts a second term from the first term.

This second term describes the expected number of connections within each group if we would redraw the network with the same number of connections per point, but make the connections randomly. Then the division into only one community is not too good anymore. For only one community, we already expected that all connections are within that same community, so the modularity of the one single community is equal to zero. Modularity, therefore, measures how many more connections there are within the communities than we actually expected.

### NETWORKS

NETWORKS has collaborated with four more scientists to make posters about their research for IMAGINARY. The three other posters concern the following topics:

• Dispatching experts to do maintenance. The poster was created by Stella Kapodistria, assistant professor in the section Stochastics of the Department of Mathematics and Computer Science at the Eindhoven University of Technology, and Peter Verleijsdonk, Doctoral Candidate at the Eindhoven University of Technology. Want to read more about this poster? Have a look at this post!
• From tweets to communication networks. The poster was created by Anna Priante, assistant professor at the Department of Technology and Operations Management (Business InformationManagement section) at the Rotterdam School of Management, Erasmus University.

#### WHERE AND WHEN?

Where When
Eindhoven Februari 14 - March 2, 2023
Groningen, Zernike Campus April 1 to 23, 2023
Amsterdam May 2023
Maastricht June/July 2023

If you want to see the posters, then pick a day and go to the exhibition. If you can't wait until the exhibition comes to your city, you can combine the visit with a day trip to Eindhoven!

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