Symmetry in Complex Networks

Many real world networks are symmetric. In the research conducted by Ben McArthur, Sanchez-Garcia and Anderson, they’ve found out that a certain degree of symmetry is also ubiquitous in complex systems. They investigated the origin and form of real-world network symmetry and its effect on network function.

Many networks – for example the internet and the world-wide web are “growing” (that is new vertices are added to the network over time). Generally any growth process which allows for new vertices to the network one at a time generally leads to a network with locally-tree-like regions. Such locally tree-like areas are common in real-world networks and their presence is important because while majority of large graphs are assymetric, it is common for large random trees to exhibit a high degree of symmetry, deriving from presence of identical branches about the same fork. Thus, we can expect that certain degree of tree-like symmetry to be present in many real-world networks.