Project List: HW 1 Network Analysis

Peter Sullivan

Load in DATA. This is the Airport DATA from the Google drive.

load(file = "USAirports.rda")

Looking at Nodes and Edges:

ls()

[1] "network_edgelist" "network_igraph"   "network_nodes"   

[4] "network_statnet"

vcount(network_igraph)

[1] 755

ecount(network_igraph)

[1] 23473

print(network_statnet)

 Network attributes:

  vertices = 755 

  directed = TRUE 

  hyper = FALSE 

  loops = FALSE 

  multiple = FALSE 

  bipartite = FALSE 

  total edges= 8228 

    missing edges= 0 

    non-missing edges= 8228 



 Vertex attribute names: 

    City Distance vertex.names 



 Edge attribute names not shown

#print(network_igraph)

plot(network_statnet)

Right off the bat, it looks like the igraph and statnet variables are showing different edges. The network igraph is showing 755 nodes and 23473 edges. The network statnet is showing 755 nodes, and 8228 edges.

Weighted, Directed, Single Mode Network?

is_bipartite(network_igraph)

[1] FALSE

is_directed(network_igraph)

[1] TRUE

is_weighted(network_igraph)

[1] FALSE

Using the Network Igraph set, we have a single mode network, which is directed, and is not weighted.

Looking at Vertex and Edge Attributes:

vertex_attr_names(network_igraph)

[1] "name"     "City"     "Position"

network::list.vertex.attributes(network_statnet)

[1] "City"         "Distance"     "na"           "vertex.names"

edge_attr_names(network_igraph)

[1] "Carrier"    "Departures" "Seats"      "Passengers" "Aircraft"  

[6] "Distance"

network::list.edge.attributes(network_statnet)

[1] "Aircraft"   "Carrier"    "Departures" "Distance"   "na"        

[6] "Passangers" "Seats"      "weight"

Igraph Attribute Names: name, City, Position

Igraph edge names: Carrier, Departures, Seats, Passengers, Aircraft, Distance

Statnet attribute names: City, Distance, na, vertex.names

statnet edge names: Aircraft, Carrier, Departures, Distance, na, Passangers, Seats, weight

Accessing Attribute DATA:

V(network_igraph)$name %>% head()

[1] "BGR" "BOS" "ANC" "JFK" "LAS" "MIA"

V(network_igraph)$City %>% head()

[1] "Bangor, ME"    "Boston, MA"    "Anchorage, AK" "New York, NY" 

[5] "Las Vegas, NV" "Miami, FL"

V(network_igraph)$Position %>% head()

[1] "N444827 W0684941" "N422152 W0710019" "N611028 W1495947"

[4] "N403823 W0734644" "N360449 W1150908" "N254736 W0801726"

(network_igraph)$Carrier %>% head()

NULL

head(network_statnet %v% "vertex.names")

[1] "1G4" "A23" "A27" "A29" "ABE" "ABI"

head(network_statnet %v% "City")

[1] "Bangor, ME"    "Boston, MA"    "Anchorage, AK" "New York, NY" 

[5] "Las Vegas, NV" "Miami, FL"

head(network_statnet %e% "weight")

[1] "193"  "253"  "141"  "3135" "4097" "1353"

Summarizing Attribute DATA

summary(E(network_igraph)$Distance)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 

      0     223     496     639     903    6089

summary(network_statnet %e% "Distance")

   Length     Class      Mode 

     8228 character character

The way the summary function worked on the statnet set makes me think the statnet dataset is incorrectly set up at the moment.
#### Dyad Census

dyad.census(network_igraph)

$mut

[1] 10449



$asym

[1] 2574



$null

[1] 271612

sna::dyad.census(network_statnet)

      Mut Asym   Null

[1,] 3605 1018 280012

Triad Census

triad.census(network_igraph)

 [1] 68169544   665870  2427052     1445     1289     2465    15322

 [8]    19171       91       39   114868      202      376      558

[15]     6422    18671

sna::triad.census(network_statnet)

          003    012     102 021D 021U 021C  111D  111U 030T 030C

[1,] 68169544 712579 2380343 1445 1289 2465 15322 19171   91   39

        201 120D 120U 120C  210   300

[1,] 114868  202  376  558 6422 18671

Transivity

transitivity(network_igraph)

[1] 0.3384609

gtrans(network_statnet)

[1] 0.3266617

The transitivity for igraph and statnet data sets were pretty close.

Local Transivity

first_five_names <- V(network_igraph)$name %>% head(5)

first_five_names

[1] "BGR" "BOS" "ANC" "JFK" "LAS"

first_five_transivity <- transitivity(network_igraph, type = "local", vids = V(network_igraph)[first_five_names])



cbind(first_five_names,first_five_transivity)

     first_five_names first_five_transivity

[1,] "BGR"            "0.581818181818182"  

[2,] "BOS"            "0.35292389068469"   

[3,] "ANC"            "0.0824960338445267" 

[4,] "JFK"            "0.385964912280702"  

[5,] "LAS"            "0.223852116875373"

transitivity(network_igraph, type = "global")

[1] 0.3384609

transitivity(network_igraph, type = "average")

[1] 0.6452844

LA seems to have low transivity while BGR has the highest at .58.

Distances in the Network

distances(network_igraph, "BGR","BOS")

    BOS

BGR   1

distances(network_igraph,"BOS", "ANC")

    ANC

BOS   2

average.path.length(network_igraph)

[1] 3.52743

average.path.length(network_igraph, directed = F)

[1] 3.447169

Identifying Isolates

names(igraph::components(network_igraph))

[1] "membership" "csize"      "no"

components(network_igraph)$no

[1] 6

components(network_igraph)$csize

[1] 745   2   2   3   2   1

components(network_igraph)$membership %>% head()

BGR BOS ANC JFK LAS MIA 

  1   1   1   1   1   1

#Isolates

isolates(network_statnet)

[1] 166

as.vector(network_statnet %v% "vertex.names")[c(isolates(network_statnet))]

[1] "DET"

Detroit seems to be the only isolate.

HW 1 Network Analysis