FIRST-PASSAGE PERCOLATION ON THE RANDOM GRAPH

Authors:
Remco Van Der Hofstad;Gerard Hooghiemstra;Piet Van Mieghem
Affiliations:
ITS, Department of Mathematics, Delft University of Technology, 2628 CD Delft, The Netherlands, E-mail: R.W.vanderHofstad@its.tudelft.nl;ITS, Department of Mathematics, Delft University of Technology, 2628 CD Delft, The Netherlands, E-mail: G.Hooghiemstra@its.tudelft.nl;ITS, Department of Electrical Engineering, Delft University of Technology, 2628 CD Delft, The Netherlands, E-mail: p.vanmieghem@its.tudelft.nl
Venue:
Probability in the Engineering and Informational Sciences
Year:
2001

Citing 2
Cited 11

Small worlds: the dynamics of networks between order and randomness

Small worlds: the dynamics of networks between order and randomness
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

On the efficiency of multicast

IEEE/ACM Transactions on Networking (TON)
On the covariance of the level sizes in random recursive trees

Random Structures & Algorithms
PATHS IN THE SIMPLE RANDOM GRAPH AND THE WAXMAN GRAPH

Probability in the Engineering and Informational Sciences
Performance analysis of the AntNet algorithm

Computer Networks: The International Journal of Computer and Telecommunications Networking
The weight of the shortest path tree

Random Structures & Algorithms
Weight of the shortest path to the first encountered peer in a peer group of size m

Probability in the Engineering and Informational Sciences
The observable part of a network

IEEE/ACM Transactions on Networking (TON)
Sampling networks by the union of m shortest path trees

Computer Networks: The International Journal of Computer and Telecommunications Networking
The effect of peer selection with hopcount or delay constraint on peer-to-peer networking

NETWORKING'08 Proceedings of the 7th international IFIP-TC6 networking conference on AdHoc and sensor networks, wireless networks, next generation internet
First-passage percolation on a width-2 strip and the path cost in a VCG auction

WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Potential networks, contagious communities, and understanding social network structure

Proceedings of the 22nd international conference on World Wide Web

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study first-passage percolation on the random graph Gp(N) with exponentially distributed weights on the links. For the special case of the complete graph, this problem can be described in terms of a continuous-time Markov chain and recursive trees. The Markov chain X(t) describes the number of nodes that can be reached from the initial node in time t. The recursive trees, which are uniform trees of N nodes, describe the structure of the cluster once it contains all the nodes of the complete graph. From these results, the distribution of the number of hops (links) of the shortest path between two arbitrary nodes is derived.We generalize this result to an asymptotic result, as N → ∞, for the case of the random graph where each link is present independently with a probability pN as long as NpN/(log N)3 → ∞. The interesting point of this generalization is that (1) the limiting distribution is insensitive to p and (2) the distribution of the number of hops of the shortest path between two arbitrary nodes has a remarkable fit with shortest path data measured in the Internet.