TY - CHAP

T1 - Degree distribution of the FKP network model

AU - Berger, Noam

AU - Bollobás, Béla

AU - Borgs, Christian

AU - Chayes, Jennifer

AU - Riordan, Oliver

PY - 2003

Y1 - 2003

N2 - Recently, Fabrikant, Koutsoupias and Papadimitriou [7] introduced a natural and beautifully simple model of network growth involving a trade-off between geometric and network objectives, with relative strength characterized by a single parameter which scales as a power of the number of nodes. In addition to giving experimental results, they proved a power-law lower bound on part of the degree sequence, for a wide range of scalings of the parameter. Here we prove that, despite the FKP results, the overall degree distribution is very far from satisfying a power law. First, we establish that for almost all scalings of the parameter, either all but a vanishingly small fraction of the nodes have degree 1, or there is exponential decay of node degrees. In the former case, a power law can hold for only a vanishingly small fraction of the nodes. Furthermore, we show that in this case there is a large number of nodes with almost maximum degree. So a power law fails to hold even approximately at either end of the degree range. Thus the power laws found in [7] are very different from those given by other internet models or found experimentally [8].

AB - Recently, Fabrikant, Koutsoupias and Papadimitriou [7] introduced a natural and beautifully simple model of network growth involving a trade-off between geometric and network objectives, with relative strength characterized by a single parameter which scales as a power of the number of nodes. In addition to giving experimental results, they proved a power-law lower bound on part of the degree sequence, for a wide range of scalings of the parameter. Here we prove that, despite the FKP results, the overall degree distribution is very far from satisfying a power law. First, we establish that for almost all scalings of the parameter, either all but a vanishingly small fraction of the nodes have degree 1, or there is exponential decay of node degrees. In the former case, a power law can hold for only a vanishingly small fraction of the nodes. Furthermore, we show that in this case there is a large number of nodes with almost maximum degree. So a power law fails to hold even approximately at either end of the degree range. Thus the power laws found in [7] are very different from those given by other internet models or found experimentally [8].

UR - http://www.scopus.com/inward/record.url?scp=35248850625&partnerID=8YFLogxK

U2 - 10.1007/3-540-45061-0_57

DO - 10.1007/3-540-45061-0_57

M3 - Chapter

AN - SCOPUS:35248850625

SN - 3540404937

SN - 9783540404934

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 725

EP - 738

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Baeten, Jos C. M.

A2 - Lenstra, Jan Karel

A2 - Parrow, Joachim

A2 - Woeginger, Gerhard J.

PB - Springer Verlag

ER -