13 Network analysis

• scale-free

• Band

• Block

• Cluster

• Multi-Hub

• Erdöl-Renyi (random)

-> Real world cannot be resembled by one type!

• can we define properties that are easy to understand and discriminative for graphs?

  • Nr. Of nodes

  • Nr. Of edges

• How to compare graphs in a tractable manner?

  • Pairwise distance

  • Sum of edges (only if weighted)

• Are there generative graph models that can lead to the observed graphs?

• Can we find network properties that are common to all (or most) networks across habitats?

  • Nodes (OTUs)

• Are certain OTUs (nodes) generally more important than others?

  • Depends on the question we want to answer with analysis

• How do (microbiological) ecological networks relate to other ecological networks (food webs, etc)?

• Is there a simple generative (microbial) network model that fits the inferred networks?

• tendency of connected nodes to belong to the same category

• Phylogeny [-1:1]

• Dijkstra algorithm

• Run time: O(|V|^2)

• random

• circular

• force directed

  • strength of connection gives length of edge

• probability if there are 2 edges between 3 nodes, whether there is a 3rd edge

• thing with triangle and triplets

  
  

• regular network with a bit increased randomness (rewiring)

• characteristic path length improved with only a bit rewiring

  
  

• Erdös-Renyi/scale-free graph model

• Watts-Strogatz graph model

• Geometric Random graph model

• STICKY (Configuration model) Graph

  • nodes have a node degree O(i) f.e.

  • edge or not is determined by product of probabilities of the two nodes

• calculate distance to its own and distance to other clusters for each point in a cluster

• average above graph gives modularity scale