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Informatics tools in network science

seminar 3 Measurements. Informatics tools in network science. Network Topology. Simple examples. What else? Network Skeleton Visualization (largescale?) Fractal properties Etc. Degree centrality. 6. 1. 3. 4. 5. 7. 2. Network degree centrality. n*: node with highest degree.

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Informatics tools in network science

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  1. seminar 3 Measurements Informatics tools in network science

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

  3. Degree centrality 6 1 3 4 5 7 2

  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 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 sum average 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

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