Connectivity and Nestedness in Bipartite Networks from Community Ecology

Bipartite networks and the nestedness concept appear in two different contexts in theoretical ecology: community ecology and islands biogeography. From a mathematical perspective nestedness is a pattern in a bipartite network. There are several nestedness indices in the market, we used the index ν. The index ν is found using the relation ν = 1 − τ where τ is the temperature of the adjacency matrix of the bipartite network. By its turn τ is defined with help of the Manhattan distance of the occupied elements of the adjacency matrix of the bipartite network. We prove that the nestedness index ν is a function of the connectivities of the bipartite network. In addition we find a concise way to find ν which avoid cumbersome algorithm manupulation of the adjacency matrix.