TY - CHAP

T1 - The big friendly giant

T2 - the giant component in clustered random graphs

AU - Berchenko, Yakir

AU - Artzy-Randrup, Yael

AU - Teicher, Mina

AU - Stone, Lewi

N1 - Publisher Copyright:
© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009.

PY - 2009/1/1

Y1 - 2009/1/1

N2 - Network theory is a powerful tool for describing and modeling complex systems having applications in widelydiffering areas including epidemiology [16], neuroscience [34], ecology [20] and the Internet [26]. In its beginning, one often compared an empirically given network, whose nodes are the elements of the system and whose edges represent their interactions, with an ensemble having the same number of nodes and edges, the most popular example being the random graphs introduced by Erdos and Renyi [11]. As the field matured, it became clear that the naive model above needed to be refined, due to the observation that real-world networks often differ significantly from the Erdos–Renyi random graphs in having a highly heterogenous non-Poisson degree distribution [5, 15] and in possessing a high level of clustering [33]. Methods for generating random networks with arbitrary degree distributions and for calculating their statistical properties are now well understood.

AB - Network theory is a powerful tool for describing and modeling complex systems having applications in widelydiffering areas including epidemiology [16], neuroscience [34], ecology [20] and the Internet [26]. In its beginning, one often compared an empirically given network, whose nodes are the elements of the system and whose edges represent their interactions, with an ensemble having the same number of nodes and edges, the most popular example being the random graphs introduced by Erdos and Renyi [11]. As the field matured, it became clear that the naive model above needed to be refined, due to the observation that real-world networks often differ significantly from the Erdos–Renyi random graphs in having a highly heterogenous non-Poisson degree distribution [5, 15] and in possessing a high level of clustering [33]. Methods for generating random networks with arbitrary degree distributions and for calculating their statistical properties are now well understood.

UR - http://www.scopus.com/inward/record.url?scp=85027971771&partnerID=8YFLogxK

U2 - 10.1007/978-0-8176-4751-3_14

DO - 10.1007/978-0-8176-4751-3_14

M3 - Chapter

AN - SCOPUS:85027971771

T3 - Modeling and Simulation in Science, Engineering and Technology

SP - 237

EP - 252

BT - Modeling and Simulation in Science, Engineering and Technology

PB - Springer Basel

ER -