Exotic phase transitions of k-cores in clustered networks

14 Oct 2016  ·  Bhat Uttam, Shrestha Munik, Hébert-Dufresne Laurent ·

The giant $k$-core --- maximal connected subgraph of a network where each node has at least $k$ neighbors --- is important in the study of phase transitions and in applications of network theory. Unlike Erd\H{o}s-R\'enyi graphs and other random networks where $k$-cores emerge discontinuously for $k\ge 3$, we show that transitive linking (or triadic closure) leads to 3-cores emerging through single or double phase transitions of both discontinuous and continuous nature... We also develop a $k$-core calculation that includes clustering and provides insights into how high-level connectivity emerges. read more

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