Quantitative Measures of Network Complexity

The first attempts to evaluate quantitatively the complexity of a system have been related to complexity of cells, organisms, and humans. Fascinated by the complex nature of the living things, a group of young mathematical biologists applied in the 1950s the Shannon theory of communications 1 to assess the information content of the living matter. The analysis made by Rashewsky 4 provided the first proof that life on earth cannot emerge as a random event, because the probability for such an event would be incredibly small. Two different approaches have been used in defining the information content. The first one proceeded from the elemental composition of the living matter (C, N, O, etc.) and is the predecessor of what is nowadays called compositional complexity. Rashewsky' topological information has been based on partitioning the atoms in a structure according to both their chemical nature and their equivalent topological neighborhoods. Mowshovitz 6 developed further these ideas to define complexity of graphs. Minoli 7