#10 Micropatterns, Macroeffects: The Physics of Complex Connectivity

In our daily lives, we often see systems made up of many parts that interact with each other — like social networks, power grids, the internet, or even biological systems. In these cases, it’s not just the parts themselves that matter, but how they are connected. These connections can lead to interesting and sometimes unexpected behaviors.

To study these kinds of systems, scientists use complex network theory. This is a mathematical way to look at systems as networks: collections of nodes (which represent things like people, machines, or cells) connected by links (which represent interactions or relationships between them).

Complex networks appear in many areas: In social networks, people are connected through friendships or communication. In power grids, power stations and homes are connected by wires. In biological systems, proteins interact with each other in cells.

One important idea in this area is the study of motifs — small patterns of connections that show up again and again in different networks. Examples include:

• Triangles, where three nodes are all connected to each other.

• Chains, where each node connects to the next in a line.

• Squares or more complex shapes in higher-dimensional networks.

  
  

These motifs help determine how the whole network behaves influencing how easily information or energy can flow through it and how resilient the network is — that is, how well it can keep working if some parts fail or are removed.

In this project, we’ll explore how different motifs affect degree correlations — for example, whether nodes with many connections tend to link to other highly connected nodes (assortativity) or not (disassortativity). How the presence of these motifs changes the network’s resilience — especially when nodes are removed either at random or in a targeted way (for example, removing the most connected nodes first).