Mathematicians can be fascinated by the elegance and beauty of the ideas behind mathematical theories. Mathematical structures are already out there and our goal is to discover them.
Wireless communication networks play a crucial role in connecting laptops, smartphones, sensors and countless physical devices, and in exchanging data among persons, computer brains and other parts of our information society.
A graph consists of objects called vertices and connections between them called edges. For every vertex, we can count how many neighbors it has, which is called its degree.
The graph isomorphism problem asks the computer to see if two graphs (simple networks) can be made to look precisely the same if the computer is only allowed to slide the nodes and stretch the connections (so the computer is not allowed to draw or or erase nodes or connections).
One beautiful, extremely important hidden network is the network of gene interactions: our DNA contains tens of thousands of genes. Some of these are really important. If you don’t have even one of them, you can’t live.
![By Hennah, Porteous - [The DISC1 Pathway Modulates Expression of Neurodevelopmental, Synaptogenic and Sensory Perception Genes http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0004906], CC BY 2.5, https://commons.wikimedia.org/w/index.php?curid=7681986](https://www.networkpages.nl/wp-content/uploads/2016/11/Network_of_how_100_of_the_528_genes_identified_with_significant_differential_expression_relate_to_DISC1_and_its_core_interactors-220x110.png)