egder

Egder is a term used in theoretical discussions of agent-based models and network diffusion to denote a unit of influence associated with a directed edge in a graph. In many models, an egder represents the potential for an agent A to affect agent B's state when they are connected.

The state of an egder can be active or inactive, and activation results from a threshold condition based on the states of neighboring agents or exogenous inputs. When activated, the egder contributes to the probability that the connected agent will switch state, often through a function that aggregates influence across the neighborhood.

Egder is not a physical object; it is an abstract construct used to study how information, behaviors, or diseases propagate through a network. The term is more common in discussions of threshold models and cascade phenomena, where edge-based influence is distinguished from node-based susceptibility. Etymology is uncertain; the coinage likely combines 'edge' (as in graph edges) with a nominal suffix to denote a unit or agent.

The concept has several variants in the literature, including continuous-valued influence and discrete activation. In practice, egder-based formulations help compare the effects of network structure, such as degree distribution or clustering, on diffusion outcomes. There are no universally adopted standards for defining egder dynamics, and the concept is primarily used in academic and educational contexts to illustrate edge-centric diffusion processes.