Exponential network

An exponential network is a network whose degree distribution decreases exponentially with degree, making highly connected nodes rare and typical degrees relatively similar.

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Degree distribution: A probability distribution describing how many connections network nodes have. It is the defining statistic used to classify an exponential network.
Erdős–Rényi model: A random graph model in which each possible edge is independently included with a fixed probability. Its sparse graphs provide a standard route to an exponential-like degree distribution.
Scale-free network: A network with a degree distribution following a power law over a substantial range. Power-law tails make very high-degree nodes far more common than in exponential networks.
Erdős–Rényi random graph: A random graph formed by independently connecting each pair of vertices with equal probability. Its degree statistics are a canonical example of a non-hub-dominated network.
Power-law testing: Statistical methods for assessing whether data follow a power-law distribution. Reliable comparison is needed before classifying an observed tail as exponential instead.
Graph theory: The mathematical study of graphs, structures made of vertices and edges. Exponential networks are graphs characterized by how their edges are distributed.
Exponential random graph model: A statistical model assigning graph probabilities through an exponential function of network statistics. Despite its name, it is a modeling framework, not a network defined by exponential degree decay.
Small-world network: A network combining short typical path lengths with strong local clustering. Small-world structure can coexist with an exponential degree distribution, but describes different properties.
Communication network: A network whose nodes and links represent communication entities and their connections. Some communication systems have degree distributions with characteristic scales rather than extreme hubs.
Finite-size scaling: A method for inferring large-system behavior from measurements on finite systems. Small networks can conceal the asymptotic form of their degree distributions.