We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates ...

Exponential graphs are graphs in the form \(y = k^x\). These graphs increase rapidly in the \(y\) direction and will never fall below the \(x\)-axis.

Exponential graphs are graphs in the form \(y = k^x\). These graphs increase rapidly in the \(y\) direction and will never fall below the \(x\)-axis.

The statistical physics of graphs and partition functions represents a vibrant intersection of graph theory, statistical mechanics and computational complexity. By summing over an ensemble of ...