Summary statistics for weighted graphs

[horaciobam]

Undirected or directed.

[horaciobam]

More common summary statistics used for Network analysis:

• [X] Degree: Number of connections of each node
• [X] Density: Ratio of actual edges to all possible edges
• [ ] Shortest path: Shortest possible series of nodes and edges that stand between any two nodes
• [ ] Diameter: Longest of all shortest paths
• [x] Transitivity: Ratio of all actual triangles over possible triangles
• [x] Centrality: More important nodes (more connections)

Note: We should measure number of overlapping edges in relation with adjacent edges for all the network and for each node. From our .dot plot we can differentiate adjacent from overlapping edges based on color:

digraph {
    graph [outputorder=endgesfirst]
    1 [color="#F8766D" fixedsize=true fontname="Courier-Bold" fontsize=85 height=2.7284509239574835 style=filled width=2.7284509239574835]
    1 -> 2 [arrowsize=0.01 color=grey76 len=10 penwidth=22]
    1 -> 3 [arrowsize=0.01 color=grey76 len=10 penwidth=6]
    1 -> 12 [arrowsize=0.01 color=grey76 len=10 penwidth=5]
    1 -> 10 [arrowsize=0.01 color=grey76 len=10 penwidth=4]
    1 -> 1 [arrowsize=0.01 color=grey76 len=10 penwidth=3]
    1 -> 6 [arrowsize=0.01 color=grey76 len=10 penwidth=2]
    1 -> 8 [arrowsize=0.01 color=grey76 len=10 penwidth=2]
    1 -> 5 [arrowsize=0.01 color=grey76 len=10 penwidth=12]
    1 -> 4 [arrowsize=0.01 color=grey76 len=10 penwidth=3]
    1 -> 11 [arrowsize=0.01 color=grey76 len=10 penwidth=1]
    1 -> 7 [arrowsize=0.01 color=grey76 len=10 penwidth=2]
    1 -> 13 [arrowsize=0.01 color=grey76 len=10 penwidth=1]
    1 -> 7 [arrowsize=0.01 color="#143D59" len=10 penwidth=1]
    1 -> 1 [arrowsize=0.01 color="#143D59" len=10 penwidth=1]
    1 -> 10 [arrowsize=0.01 color="#143D59" len=10 penwidth=1]
    2 [color="#E18A00" fixedsize=true fontname="Courier-Bold" fontsize=85 height=3.5433819375782165 style=filled width=3.5433819375782165]
    2 -> 1 [arrowsize=0.01 color=grey76 len=10 penwidth=13]
    2 -> 7 [arrowsize=0.01 color=grey76 len=10 penwidth=7]
    2 -> 3 [arrowsize=0.01 color=grey76 len=10 penwidth=12]
    2 -> 8 [arrowsize=0.01 color=grey76 len=10 penwidth=13]
    2 -> 10 [arrowsize=0.01 color=grey76 len=10 penwidth=10]
    2 -> 4 [arrowsize=0.01 color=grey76 len=10 penwidth=7]
    2 -> 12 [arrowsize=0.01 color=grey76 len=10 penwidth=28]
    2 -> 13 [arrowsize=0.01 color=grey76 len=10 penwidth=10]
    2 -> 11 [arrowsize=0.01 color=grey76 len=10 penwidth=2]
    2 -> 2 [arrowsize=0.01 color=grey76 len=10 penwidth=6]
    2 -> 9 [arrowsize=0.01 color=grey76 len=10 penwidth=3]
    2 -> 6 [arrowsize=0.01 color=grey76 len=10 penwidth=2]
    2 -> 1 [arrowsize=0.01 color="#143D59" len=10 penwidth=1]
    2 -> 10 [arrowsize=0.01 color="#143D59" len=10 penwidth=1]

I can also get the statistics directly from the new_viz_ovrf.py script itself.

[horaciobam]

Try using NetworkX

[horaciobam]

Maybe use graph kernels?

[horaciobam]

Mean kmer distance (> mean(upper.tri(km))):

Family	Mean kmer distance	Baltimore group
Adenoviridae	0.4997828	dsDNA
Coronaviridae	0.4991135	(+) ssRNA
Mononegavirales	0.4997619	(-) ssRNA
Reoviridae	0.4994664	dsRNA
Retroviridae	0.4985549	Retrovirus
Rhabdoviridae	0.4995567	(-) ssRNA

[horaciobam]

Double check the results. Are data files correct? Interpreted as double instead of integers. Take upper.tri and get a limited part of it. Index the matrix itself.

[horaciobam]

Corrected mean kmer distance by using:

for (d in All) {
  up  <- upper.tri(d)
  m <- mean(d[up])
  print(m)
}

Family	Mean kmer distance	Baltimore group	Host	Number of complete ref genomes
Adenoviridae	0.2317234	dsDNA	Human, Non-human vertebrate	72
Coronaviridae	0.2101119	(+) ssRNA	Human, Non-human vertebrate	65
Mononegavirales	0.2559121	(-) ssRNA	Human, Non-human vertebrate	327
Reoviridae	0.2877149	dsRNA	Human, Non-human vertebrate, invertebrate, plants	887
Retroviridae	0.26761	Retrovirus	Human, Non-human vertebrate	93
Rhabdoviridae	0.2489143	(-) ssRNA	Human, Non-human vertebrate, invertebrate, plants	82

[horaciobam]

Full Table with all evaluated families in fam_analysis.csv on the data folder