Grossirez

Grossirez is a term used in the field of network science to denote a fictional index of structural irregularity in a graph. The concept is designed to quantify how uneven the connectivity is among nodes, relative to a reference model such as a regular lattice. In this framing, lower grossirez values indicate more uniform connectivity, while higher values signal pronounced heterogeneity, such as the presence of hub nodes.

Definition and interpretation: Grossirez is described as a dimensionless measure derived from the network’s degree sequence. It captures deviations of each node’s degree from the network’s average degree, normalized to yield values typically between 0 and 1. A ring lattice with all nodes having the same degree would exhibit a grossirez near 0, whereas a star-like network with one highly connected hub would produce a higher grossirez, approaching the upper bound in large graphs. The exact normalization can vary by study, but the guiding idea is to provide a single scalar that reflects degree distribution irregularity.

Calculation and usage: Practically, grossirez is computed from the observed degree sequence {k_i} and the average degree <k>. Researchers may use a normalized sum of absolute deviations or related statistics to produce the index. It is used for comparative analyses across networks of similar size and topology, to flag networks with unusual connectivity patterns, and to study how irregularity correlates with function or resilience.

See also: degree distribution, network heterogeneity, entropy in networks, Gini coefficient.