Degrees in graphs I: the Handshake Lemma
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.
A big breakthrough in the Graph Isomorphism Problem
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).
Networks to understand our DNA
![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-1024x666.png)
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.