Source-linked AI summary
Temporal effects in the growth of networks
Matus Medo, Giulio Cimini, Stanislao Gualdi
TL;DR
Preferential attachment models do not adequately account for temporal effects, motivating a model that combines heterogeneous node fitness with fitness decay. The model and citation data support varied degree distributions, including power-law tails under specified relevance distributions.
Problem
Preferential attachment predicts a strong age–degree relation that is unrealistic in some systems, motivating a model that accounts for temporal effects alongside node heterogeneity.
Source: p. 1Method
The paper models preferential attachment using heterogeneous node relevance that decays over time, and derives degree distributions under different relevance assumptions.
Source: pp. 1–2Results
An exponential total-relevance tail yields a degree-distribution power law with exponent 3; a mixed relevance distribution produces exponents from 2.44 to 4.18.
Source: p. 3Takeaways & Limitations
The model produces varied realistic degree distributions, and the citation data support coexisting node heterogeneity and time decay.
Source: p. 4The model omits directedness, accelerating network growth, and fragmentation, and leaves cases without stationary normalization open.
Source: p. 4
Abstract
from arXiv · showhide
We show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PA-based models assumed either heterogeneity or decay in isolation, we propose a simple analytically treatable model that combines these two factors. Depending on the input assumptions, the resulting degree distribution shows an exponential, log-normal or power-law decay, which makes the model an apt candidate for modeling a wide range of real systems.