plum pudding models for growing small-world networks
DESCRIPTION
Plum Pudding Models for Growing Small-World Networks. Image Credit to transductions.net. Ari Zitin (University of North Carolina), Alex Gorowara (Worcester Polytechnic Institute) S. Squires, M. Herrera, T. Antonsen , M. Girvan, E. Ott (University of Maryland). Motivation and Background. - PowerPoint PPT PresentationTRANSCRIPT
Plum Pudding Models for Growing Small-World NetworksAri Zitin (University of North Carolina), Alex Gorowara (Worcester Polytechnic Institute)
S. Squires, M. Herrera, T. Antonsen, M. Girvan, E. Ott (University of Maryland)
Image Credit to transductions.net
Motivation and Background● Small-World Networks
– Path lengths are short (grow logarithmically or slower with the number of nodes N)
– Clustering (probability that a node's neighbors are connected to each other) is high
● Real networks grow in spatial dimensions– Neurological and cellular networks exist, expand, and connect in three
dimensions of space– The formation of new connections between nodes is limited by proximity
Small-world modelLattice Random
Image from Watts-Strogatz Nature 1998
Our Models● We place new nodes in a
ball (the Plum Pudding Network Model) or on a sphere (the Thomson Network Model) of d dimensions
● Each new node connects to its m nearest neighbors
● Nodes repel each other until they achieve a roughly uniform spatial distribution
Image from Wikimedia Commons
1-Dimensional Thomson Network
Images from Ozik et. al.Physical Review E 2004
Addition of a New Node to the 2-D Plum Pudding Network
Path Length is Logarithmic in Plum Pudding Network Model
2D
4D
8D
Clustering Decays with Dimension in Plum Pudding Network Model
High Clustering
Low Clustering
General Results
● Different models (Plum vs. Thomson) of the same dimension have similar characteristics
Some contribution due to edge effects
● Consistent small-world characteristics
Logarithmic path length, asymptotic clustering
● Substantial differences due to dimension
Approaches “dimensionless” behavior as the dimension grows large
● Applications to neuronal networks
With Thanks to J. J. Thomson
Image from Wikimedia Commons