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 ...

Data from an experiment may result in a graph indicating exponential growth. This implies the formula of this growth is \(y = k{x^n}\), where \(k\) and \(n\) are constants. Using logarithms, we can ...

Political Analysis, Vol. 19, No. 1 (Winter 2011), pp. 66-86 (21 pages) Methods for descriptive network analysis have reached statistical maturity and general acceptance across the social sciences in ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...

Before reading this guide, you may find it helpful to read the guide on graphs from Module 7 (M7) and the guide on indices from Module 8 (M8). In Module 7 (M7) Graphs, you learned that simultaneous ...

The Lambert W function, defined as the inverse of the function W ↦ W e^W, plays a crucial role in resolving equations where the variable appears both in linear and exponential forms. Its mathematical ...