1. Community Structure In Time-Dependent, Multiscale, And Multiplex Networks
Peter J. Mucha, Thomas Richardson, Kevin Macon, Mason A. Porter, Jukka-Pekka Onnela
Name, affliation, why are you here? (hopefully not just to sleep)
There will be a quiz!
Science 14 May 2010: Vol no. 5980, pp DOI: /science
Fadi Towfic, August 16, 2010

2. Standard Evaluation of Communities
Q = Σij (Aij − Pij) δ(gi, gj)
A = adjacency matrix
P = expected weight of edge ij under some null model
δ = Indicator function, 1 if gi,gj belong to same community, 0 otherwise
Fadi Towfic, August 16, 2010

3. Standard Evaluation of Communities
An equivalent way to measure communities:
(Number of edges connecting node i to nodes within a chosen community) – (all possible edges between node i and all other nodes in the graph)
Fadi Towfic, August 16, 2010

4. Limitations No good null model for time-dependent graphs
More graphs have time-dependent components
social networks
gene-networks
computer networks
Definition of community depends on edge connectivity, how to take into account 3D?
Fadi Towfic, August 16, 2010

5. Effect Of Interslice Weights
Fadi Towfic, August 16, 2010

6. Qmultislice Parameters: γ is a resolution parameter [0-1]
2μ number of connections possible for any node across all slices
kjs is strength of node j in slice s (computed as Kjs = Σi Aijs)
ms total sum of all strengths in slice s (computed as ms = Σj kjs)
δij or δsr is an indicator function = 1 if it is possible to transition from ij or sr, 0 otherwise
δ(gis,gjr) is an indicator function = 1 if node i in slice s is in the same community as node j in slice r.
Fadi Towfic, August 16, 2010

7. Conclusions/Uses
First evaluation measure of its kind to study community detection across time in graphs
Extends Laplacian dynamics
Can help in studying community evolution across time
Not a community detection algorithm!
Network can now be dynamic (time-based, space-based…etc) instead of static entities
No current application of this method in Bioinformatics
Fadi Towfic, August 16, 2010