1. Informatics tools in network science
seminar 3
Measurements

2. Network Topology Simple examples What else? Network Skeleton
Visualization (largescale?)
Fractal properties
Etc.

3. Degree centrality 6 1 3 4 5 7 2 Node Score Standardized Score 1 1 1/6 1
 1/6 2 3  3
 3/6 = 1/2 4  2
2/6 = 1/3 5 6
 2/6  = 1/3 7
 2/6 = 1/3

4. Network degree centrality
n*: node with highest degree
Minimal:
The higher the value of the measure the higher the difference of the node with the highest Degree Centrality to all other nodes in the network is.
Infinite:

5. Betweenness Centrality
The Betweenness Centrality is the normalized number of shortest paths going through a node in a network.

6. Closeness centrality
The Closeness Centrality is the normalized number of steps required to access every other node from a given node in a network.
Length of the shortest path

7. Eigenvector centrality, PageRank

8. Clustering coefficient
Global clustering coefficient
The local clustering coefficient of a vertex in a graph quantifies how close its neighbors are to being a clique (complete graph).
C = 1/3

9. Clustering coefficient
Scale-free network
Random graph
degree distribution
(the clustering coefficient behaves the same)

10. Network motifs

11. Topological Overlap
the ratio of shared nodes over the number of nodes reachable from a particular pair of nodes
Minimal (0)
Maximal (1)

12. Diameter and Density
The Diameter considers the largest geodesic distance between any pair of nodes in a network.
The measure Density is the proportion of possible edges that are actually present in the network.

13. Module measurements Effective number of modules
Overlap value of elements (e.g. effective number of module belongs)
Bridgeness value of elements:
The bridgeness measure of an element or link as the overlap of the given element or link between two or more modules relative to the overlap of the other elements or links.
T is the area-overlap, or common area of element between modules .
The total bridgeness of element i describes the bridgeness of that element between all modules:
Module similarity of elements:
The similarity of the elements i and j is based on their module membership vectors, di and dj :

14. Network capacity
e.g. Maximal flow (minimal cut) problem

15. Robustness
Structural cohesion: how many node needs to be removed to disconnect the graph 2 1 5

16. Network connectivity Average geodesic length (the characteristic
Path length): normalized average length of all shortest path in the network
infinite in case of disconnected graph
Inverse geodesic length

17. Effective number average sum eff. num 30 30 30 25 20 20 25 27.5 165
5.975
100 60 2
27.5
165
1.570 1 1 1

18. Take home messages separate the giant component (if exists)
compare measurements (test graph families, controll networks)
use effective numbers
check distributions

19. Programs R ModuLand Pajek Cytoscape with plugins:
NetworkAnalyzer: distributions
NetMatch: Motif search
GraMoFoNe: Graph Motif For Networks
CentisCaPe: centrality values
(lényegiDB)
+ python modules

20. Python