TY - JOUR
T1 - Beyond preferential attachment
T2 - Falling of stars and survival of superstars
AU - Somin, Shahar
AU - Altshuler, Yaniv
AU - Pentland, Alex Sandy
AU - Shmueli, Erez
N1 - Publisher Copyright:
© 2022 The Authors.
PY - 2022/8/24
Y1 - 2022/8/24
N2 - Numerous studies over the past decades established that real-world networks typically follow preferential attachment and detachment principles. Subsequently, this implies that degree fluctuations monotonically increase while rising up the 'degree ladder', causing high-degree nodes to be prone for attachment of new edges and for detachment of existing ones. Despite the extensive study of node degrees (absolute popularity), many domains consider node ranks (relative popularity) as of greater importance. This raises intriguing questions-what dynamics are expected to emerge when observing the ranking of network nodes over time? Does the ranking of nodes present similar monotonous patterns to the dynamics of their corresponding degrees? In this paper, we show that surprisingly the answer is not straightforward. By performing both theoretical and empirical analyses, we demonstrate that preferential principles do not apply to the temporal changes in node ranking. We show that the ranking dynamics follows a non-monotonous curve, suggesting an inherent partition of the nodes into qualitatively distinct stability categories. These findings provide plausible explanations to observed yet hitherto unexplained phenomena, such as how superstars fortify their ranks despite massive fluctuations in their degrees, and how stars are more prone to rank instability.
AB - Numerous studies over the past decades established that real-world networks typically follow preferential attachment and detachment principles. Subsequently, this implies that degree fluctuations monotonically increase while rising up the 'degree ladder', causing high-degree nodes to be prone for attachment of new edges and for detachment of existing ones. Despite the extensive study of node degrees (absolute popularity), many domains consider node ranks (relative popularity) as of greater importance. This raises intriguing questions-what dynamics are expected to emerge when observing the ranking of network nodes over time? Does the ranking of nodes present similar monotonous patterns to the dynamics of their corresponding degrees? In this paper, we show that surprisingly the answer is not straightforward. By performing both theoretical and empirical analyses, we demonstrate that preferential principles do not apply to the temporal changes in node ranking. We show that the ranking dynamics follows a non-monotonous curve, suggesting an inherent partition of the nodes into qualitatively distinct stability categories. These findings provide plausible explanations to observed yet hitherto unexplained phenomena, such as how superstars fortify their ranks despite massive fluctuations in their degrees, and how stars are more prone to rank instability.
KW - Network dynamics
KW - Network theory
KW - Node ranking
KW - Popularity dynamics
UR - http://www.scopus.com/inward/record.url?scp=85137735160&partnerID=8YFLogxK
U2 - 10.1098/rsos.220899
DO - 10.1098/rsos.220899
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C2 - 36039282
AN - SCOPUS:85137735160
SN - 2054-5703
VL - 9
JO - Royal Society Open Science
JF - Royal Society Open Science
IS - 8
M1 - 220899
ER -