smallworldlike

Smallworldlike describes systems or networks whose structure resembles small-world networks, without necessarily meeting all formal criteria of a strict small-world model. In a smallworldlike network, a large portion of node pairs can be connected through a relatively small number of steps, while local groups of nodes exhibit substantial clustering. This combination—high local clustering with short global separation—gives rise to efficient connectivity that is often observed in complex systems.

Quantitative assessment typically involves comparing the network to a random reference with the same degree distribution. Key metrics include the clustering coefficient (C) and the characteristic path length (L). A network is considered smallworldlike if its C is markedly higher than that of the random reference (C_rand) while its L remains close to the random reference (L_rand). A commonly used composite indicator is the small-world-ness measure sigma = (C/C_rand) / (L/L_rand), with values greater than one suggesting small-worldlike structure. Some studies also use the omega metric to capture deviations from lattice and random extremes.

The term is often applied when a system shows approximate small-world features but does not strictly satisfy all thresholds, or when data are incomplete, noisy, or involve weighted or directed connections. In practice, smallworldlike networks appear across diverse domains, including social and communication networks, brain and neural networks, metabolic and ecological networks, and transportation or collaboration networks. Analysts note that true small-world properties can depend on network size, sampling, edge definitions, and temporal dynamics, so smallworldlike descriptions emphasize approximate rather than exact classification.