MULTIVARIJATNE STATISTIČKE METODE

# MULTIVARIJATNE STATISTIČKE METODE
## Predavanje 9: Network analiza
### dr.sc. Luka Šikić
### Fakultet hrvatskih studija | <a href="https://lusiki.github.io/WebMultiVar/">Github MV</a>

---

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# Pregled predavanja

1. [Općenito o network analizi](#opc)

2. [Network podatci](#netdta)

3. [Network objekt](#netob)

4. [Praktični primjer (network analiza)](#stat)

---

# OPĆENITO O NETWORK ANALIZI

(Osnova za korištenje)

---

# Koncept
<br>
<br>
<br>
- modeliranje kompleksnosti i međupovezanosti
<br>
- centralna metodologija za (digitalne) društvene i humanističke znanosti
<br>
- upotreba u analizi komunikacijskih kanala, modeliranju epidemije, razumijevanju društvenih interakcija
<br>
- vizualna analiza - *uvodno*
<br>
- statistička analiza - *napredno*

---

# Software podrška
<br>
<br>
<br>
- [statnet](http://statnet.org/)
<br>
- [igraph](https://igraph.org/)
<br>
- [tidygraph](https://github.com/thomasp85/tidygraph)
<br>
- [gggraph](https://www.data-imaginist.com/2017/ggraph-introduction-layouts/)

---

# Najbitniji elementi mreže
<br>
<br>
- nodes (*čvorovi*) i vertices (*poveznice*) ili edges i links
<br>
<br>
- atributi (*attributes*)
<br>
<br>
- adjecancy matrice vs. data.frame
<br>
<br>
- mreže mogu biti usmjerene (directed) i neusmjerene (unidirected)
<br>

---

# Čvorovi (*nodes*)
<br>
<br>
<img src="../Foto/net8.png" width="500px" style="display: block; margin: auto;" />

---

# Stvori demo network objekt (*nodes*)
<br>
<br>

```r
# node-list objekt ima jednu varijablu (kolonu) i sadržava ID oznaku za pripadajući edge
node_list <- tibble(id = 1:5) 
node_list
```

```
## # A tibble: 5 x 1
##      id
##   <int>
## 1     1
## 2     2
## 3     3
## 4     4
## 5     5
```
---

# Poveznice (*edges*)
<br>
<br>
<img src="../Foto/net9.png" width="500px" style="display: block; margin: auto;" />

---

# Stvori demo network objekt (*edges*)
<br>

```r
#  edge-list ima minimalno dvije kolone: kolona izvora čvorova (nodes) i kolona smjernica čvorova
#  edge-list objekt može sadržavati i dodatne atribute (varijable)
edge_list <- tibble(from = c(1, 2, 2, 3, 4), to = c(2, 3, 4, 2, 1))
edge_list
```

```
## # A tibble: 5 x 2
##    from    to
##   <dbl> <dbl>
## 1     1     2
## 2     2     3
## 3     2     4
## 4     3     2
## 5     4     1
```

---

# Karakteristike (*attributes*)
<br>
<br>
<img src="../Foto/net10.png" width="500px" style="display: block; margin: auto;" />

---

# Stvori demo network objekt (*attributes*)
<br>

```r
node_list_attr <- node_list %>% 
  mutate(Spol = c("F","F","M","F","M"))
node_list_attr
```

```
## # A tibble: 5 x 2
##      id Spol 
##   <int> <chr>
## 1     1 F    
## 2     2 F    
## 3     3 M    
## 4     4 F    
## 5     5 M
```

---

# Reprezentacija mreže
<br>
###### Standardni način: adjecancy matrica
<br>

```r
#>   1 2 3 4 5
#> 1 0 1 0 0 0
#> 2 0 0 1 1 0
#> 3 0 1 0 0 0
#> 4 1 0 0 0 0
#> 5 1 0 0 0 0
```
---

# *Adjecency* matrica
<br>
<img src="../Foto/net5.png" width="650px" style="display: block; margin: auto;" />

---

# *Adjecency* matrica
<br>
<img src="../Foto/net6.png" width="650px" style="display: block; margin: auto;" />

---

# Reprezentacija mreže
<br>
###### "Moderni" način: crna kutija (*black box*)
<br>

```r
g = graph_from_data_frame(edge_list, directed = FALSE, vertices = node_list)
g
```

```
## IGRAPH b7f6160 UN-- 5 5 -- 
## + attr: name (v/c)
## + edges from b7f6160 (vertex names):
## [1] 1--2 2--3 2--4 2--3 1--4
```

.footnote[[*]Postoji mnoštvo različitih načina za "black box" reprezentaciju. Upoznati ćemo nekoliko načina!]

---

# NETWORK PODATCI

(Napravi mrežu iz podataka!)

---

# Preuzmi podatke 
<br>

```r
url <- "https://github.com/jessesadler/intro-to-r/blob/master/data/correspondence-data-1585.csv"
epistole <- read_html(url) %>%
  html_table(fill = TRUE) %>%
  as.data.frame() %>%
  select(-1) %>%
  row_to_names(1)
glimpse(epistole)
```

```
## Rows: 114
## Columns: 4
## $ writer      <chr> "Meulen, Andries van der", "Meulen, Andries van der", "Meu~
## $ source      <chr> "Antwerp", "Antwerp", "Antwerp", "Antwerp", "Antwerp", "An~
## $ destination <chr> "Delft", "Haarlem", "Haarlem", "Delft", "Haarlem", "Delft"~
## $ date        <chr> "1585-01-03", "1585-01-09", "1585-01-11", "1585-01-12", "1~
```

---

# Pregledaj podatke
<br>

```r
head(epistole,15)
```

```
##                     writer  source destination       date
## 2  Meulen, Andries van der Antwerp       Delft 1585-01-03
## 3  Meulen, Andries van der Antwerp     Haarlem 1585-01-09
## 4  Meulen, Andries van der Antwerp     Haarlem 1585-01-11
## 5  Meulen, Andries van der Antwerp       Delft 1585-01-12
## 6  Meulen, Andries van der Antwerp     Haarlem 1585-01-12
## 7  Meulen, Andries van der Antwerp       Delft 1585-01-17
## 8  Meulen, Andries van der Antwerp       Delft 1585-01-22
## 9  Meulen, Andries van der Antwerp       Delft 1585-01-23
## 10    Della Faille, Marten Antwerp     Haarlem 1585-01-24
## 11 Meulen, Andries van der Antwerp       Delft 1585-01-28
## 12 Meulen, Andries van der Antwerp       Delft 1585-01-30
## 13 Meulen, Andries van der Antwerp       Delft 1585-02-05
## 14 Meulen, Andries van der Antwerp       Delft 1585-02-07
## 15   Della Faille, Jacques Haarlem       Delft 1585-02-10
## 16 Meulen, Andries van der Antwerp       Delft 1585-02-11
```

---

# Stvori node listu
<br>

```r
sources <- epistole %>%
  distinct(source) %>%
  rename(label = source)

sources
```

```
##       label
## 1   Antwerp
## 2   Haarlem
## 3 Dordrecht
## 4    Venice
## 5     Lisse
## 6  Het Vlie
## 7   Hamburg
## 8     Emden
## 9 Amsterdam
```

---

# Stvori node listu
<br>

```r
destinations <- epistole %>%
  distinct(destination) %>%
  rename(label = destination)

destinations
```

```
##        label
## 1      Delft
## 2    Haarlem
## 3  The Hague
## 4 Middelburg
## 5     Bremen
```

---

# Stvori node listu
<br>

```r
# poveži u jedan objekt
nodes <- full_join(sources, destinations, by = "label")
nodes
```

```
##         label
## 1     Antwerp
## 2     Haarlem
## 3   Dordrecht
## 4      Venice
## 5       Lisse
## 6    Het Vlie
## 7     Hamburg
## 8       Emden
## 9   Amsterdam
## 10      Delft
## 11  The Hague
## 12 Middelburg
## 13     Bremen
```

---

# Stvori node listu

```r
# dodaj ID
nodes <- nodes %>% rowid_to_column("id")
nodes
```

```
##    id      label
## 1   1    Antwerp
## 2   2    Haarlem
## 3   3  Dordrecht
## 4   4     Venice
## 5   5      Lisse
## 6   6   Het Vlie
## 7   7    Hamburg
## 8   8      Emden
## 9   9  Amsterdam
## 10 10      Delft
## 11 11  The Hague
## 12 12 Middelburg
## 13 13     Bremen
```

---

# Napravi edge listu

```r
per_route <- epistole %>%  
  group_by(source, destination) %>%
  summarise(weight = n()) %>% 
  ungroup()

head(per_route,13)
```

```
## # A tibble: 13 x 3
##    source    destination weight
##    <chr>     <chr>        <int>
##  1 Amsterdam Bremen           1
##  2 Antwerp   Delft           68
##  3 Antwerp   Haarlem          5
##  4 Antwerp   Middelburg       1
##  5 Antwerp   The Hague        2
##  6 Dordrecht Haarlem          1
##  7 Emden     Bremen           1
##  8 Haarlem   Bremen           2
##  9 Haarlem   Delft           26
## 10 Haarlem   Middelburg       1
## 11 Haarlem   The Hague        1
## 12 Hamburg   Bremen           1
## 13 Het Vlie  Bremen           1
```

---

# Napravi edge listu

```r
edges <- per_route %>% 
  left_join(nodes, by = c("source" = "label")) %>% 
  rename(from = id)
edges
```

```
## # A tibble: 15 x 4
##    source    destination weight  from
##    <chr>     <chr>        <int> <int>
##  1 Amsterdam Bremen           1     9
##  2 Antwerp   Delft           68     1
##  3 Antwerp   Haarlem          5     1
##  4 Antwerp   Middelburg       1     1
##  5 Antwerp   The Hague        2     1
##  6 Dordrecht Haarlem          1     3
##  7 Emden     Bremen           1     8
##  8 Haarlem   Bremen           2     2
##  9 Haarlem   Delft           26     2
## 10 Haarlem   Middelburg       1     2
## 11 Haarlem   The Hague        1     2
## 12 Hamburg   Bremen           1     7
## 13 Het Vlie  Bremen           1     6
## 14 Lisse     Delft            1     5
## 15 Venice    Haarlem          2     4
```

---

# Napravi edge listu

```r
edges <- edges %>% 
  left_join(nodes, by = c("destination" = "label")) %>% 
  rename(to = id)
edges
```

```
## # A tibble: 15 x 5
##    source    destination weight  from    to
##    <chr>     <chr>        <int> <int> <int>
##  1 Amsterdam Bremen           1     9    13
##  2 Antwerp   Delft           68     1    10
##  3 Antwerp   Haarlem          5     1     2
##  4 Antwerp   Middelburg       1     1    12
##  5 Antwerp   The Hague        2     1    11
##  6 Dordrecht Haarlem          1     3     2
##  7 Emden     Bremen           1     8    13
##  8 Haarlem   Bremen           2     2    13
##  9 Haarlem   Delft           26     2    10
## 10 Haarlem   Middelburg       1     2    12
## 11 Haarlem   The Hague        1     2    11
## 12 Hamburg   Bremen           1     7    13
## 13 Het Vlie  Bremen           1     6    13
## 14 Lisse     Delft            1     5    10
## 15 Venice    Haarlem          2     4     2
```

---

# NETWORK OBJEKT

(Osnova za analizu)

---

# Napravi mrežni objekt I

```r
library(network)
routes_network <- network(edges,
                          vertex.attr = nodes,
                          matrix.type = "edgelist",
                          ignore.eval = FALSE)
class(routes_network)
```

```
## [1] "network"
```

```r
routes_network
```

```
##  Network attributes:
##   vertices = 13 
##   directed = TRUE 
##   hyper = FALSE 
##   loops = FALSE 
##   multiple = FALSE 
##   bipartite = FALSE 
##   total edges= 15 
##     missing edges= 0 
##     non-missing edges= 15 
## 
##  Vertex attribute names: 
##     id label vertex.names 
## 
##  Edge attribute names: 
##     from to weight
```
]

---

# Vizualiziraj mrežu I

```r
plot(routes_network, vertex.cex = 3)
```

---

# Vizualiziraj mrežu II

```r
plot(routes_network, vertex.cex = 3, mode = "circle")
```

---

# Napravi mrežni objekt II

```r
detach(package:network) # ukloni paket
rm(routes_network) # Ukloni iz radnog prostora
library(igraph)
# uredi (names mora biti na prvom mjestu)
nodes %>% rename(names=label) %>% select(names,id) -> nod
# Napravi mrežni objekt
routes_igraph <- graph_from_data_frame(d = edges,
                                       vertices = nod,
                                       directed = TRUE)
routes_igraph # Pogledaj objekt
```

```
## IGRAPH b9439a0 DNW- 13 15 -- 
## + attr: name (v/c), id (v/n), weight (e/n), from (e/n), to (e/n)
## + edges from b9439a0 (vertex names):
##  [1] Amsterdam->Bremen     Antwerp  ->Delft      Antwerp  ->Haarlem   
##  [4] Antwerp  ->Middelburg Antwerp  ->The Hague  Dordrecht->Haarlem   
##  [7] Emden    ->Bremen     Haarlem  ->Bremen     Haarlem  ->Delft     
## [10] Haarlem  ->Middelburg Haarlem  ->The Hague  Hamburg  ->Bremen    
## [13] Het Vlie ->Bremen     Lisse    ->Delft      Venice   ->Haarlem
```

---

# Vizualiziraj mrežu I

```r
plot(routes_igraph, edge.arrow.size = 0.2)
```

---

# Vizualiziraj mrežu II

```r
plot(routes_igraph, layout = layout_with_graphopt, edge.arrow.size = 0.2)
```

---

# Napravi mrežni objekt III

```r
library(tidygraph)
library(ggraph)
# 1. način
routes_tidy <- tbl_graph(nodes = nodes, edges = edges, directed = TRUE)
# 2.način
routes_igraph_tidy <- as_tbl_graph(routes_igraph)
# Pregledaj objekte
class(routes_tidy)
```

```
## [1] "tbl_graph" "igraph"
```

```r
class(routes_igraph_tidy)
```

```
## [1] "tbl_graph" "igraph"
```

```r
class(routes_igraph)
```

```
## [1] "igraph"
```

---

# Pregledaj objekt
<br>
<br>
.tiny[

```r
routes_tidy
```

```
## # A tbl_graph: 13 nodes and 15 edges
## #
## # A directed acyclic simple graph with 1 component
## #
## # Node Data: 13 x 2 (active)
##      id label    
##   <int> <chr>    
## 1     1 Antwerp  
## 2     2 Haarlem  
## 3     3 Dordrecht
## 4     4 Venice   
## 5     5 Lisse    
## 6     6 Het Vlie 
## # ... with 7 more rows
## #
## # Edge Data: 15 x 5
##    from    to source    destination weight
##   <int> <int> <chr>     <chr>        <int>
## 1     9    13 Amsterdam Bremen           1
## 2     1    10 Antwerp   Delft           68
## 3     1     2 Antwerp   Haarlem          5
## # ... with 12 more rows
```
]
---

# Manipulacija sa objektom (tidyverse)
<br>
<br>
.tiny[

```r
routes_tidy %>% 
  activate(edges) %>% 
  arrange(desc(weight))
```

```
## # A tbl_graph: 13 nodes and 15 edges
## #
## # A directed acyclic simple graph with 1 component
## #
## # Edge Data: 15 x 5 (active)
##    from    to source  destination weight
##   <int> <int> <chr>   <chr>        <int>
## 1     1    10 Antwerp Delft           68
## 2     2    10 Haarlem Delft           26
## 3     1     2 Antwerp Haarlem          5
## 4     1    11 Antwerp The Hague        2
## 5     2    13 Haarlem Bremen           2
## 6     4     2 Venice  Haarlem          2
## # ... with 9 more rows
## #
## # Node Data: 13 x 2
##      id label    
##   <int> <chr>    
## 1     1 Antwerp  
## 2     2 Haarlem  
## 3     3 Dordrecht
## # ... with 10 more rows
```
]
---

# Vizualiziraj objekt I

```r
# Osnovna vizualizacija
ggraph(routes_tidy) + geom_edge_link() + geom_node_point() + theme_graph()
```

---

# Vizualiziraj objekt II

```r
# Poboljšana vizualizacija
ggraph(routes_tidy, layout = "graphopt") + 
  geom_node_point() +
  geom_edge_link(aes(width = weight), alpha = 0.8) + 
  scale_edge_width(range = c(0.2, 2)) +
  geom_node_text(aes(label = label), repel = TRUE) +
  labs(edge_width = "Letters") +
  theme_graph()
```

---

# INTERAKTIVNE VIZUALIZACIJE

---

# Interaktivne vizualizacije I

```r
options(htmltools.preserve.raw = FALSE) 
library(visNetwork)
visNetwork(nodes, edges)
```

<div id="htmlwidget-8ec0ed7f4d58e53f85df" style="width:2100px;height:900px;" class="visNetwork html-widget"></div>
<script type="application/json" data-for="htmlwidget-8ec0ed7f4d58e53f85df">{"x":{"nodes":{"id":[1,2,3,4,5,6,7,8,9,10,11,12,13],"label":["Antwerp","Haarlem","Dordrecht","Venice","Lisse","Het Vlie","Hamburg","Emden","Amsterdam","Delft","The Hague","Middelburg","Bremen"]},"edges":{"source":["Amsterdam","Antwerp","Antwerp","Antwerp","Antwerp","Dordrecht","Emden","Haarlem","Haarlem","Haarlem","Haarlem","Hamburg","Het Vlie","Lisse","Venice"],"destination":["Bremen","Delft","Haarlem","Middelburg","The Hague","Haarlem","Bremen","Bremen","Delft","Middelburg","The Hague","Bremen","Bremen","Delft","Haarlem"],"weight":[1,68,5,1,2,1,1,2,26,1,1,1,1,1,2],"from":[9,1,1,1,1,3,8,2,2,2,2,7,6,5,4],"to":[13,10,2,12,11,2,13,13,10,12,11,13,13,10,2]},"nodesToDataframe":true,"edgesToDataframe":true,"options":{"width":"100%","height":"100%","nodes":{"shape":"dot"},"manipulation":{"enabled":false}},"groups":null,"width":null,"height":null,"idselection":{"enabled":false},"byselection":{"enabled":false},"main":null,"submain":null,"footer":null,"background":"rgba(0, 0, 0, 0)"},"evals":[],"jsHooks":[]}</script>

---

# Interaktivne vizualizacije II

```r
options(htmltools.preserve.raw = FALSE) 
edges <- mutate(edges, width = weight/5 + 1)
visNetwork(nodes, edges) %>% 
  visIgraphLayout(layout = "layout_with_fr") %>% 
  visEdges(arrows = "middle")
```

<div id="htmlwidget-6999554aaf2469e7374d" style="width:2100px;height:900px;" class="visNetwork html-widget"></div>
<script type="application/json" data-for="htmlwidget-6999554aaf2469e7374d">{"x":{"nodes":{"id":[1,2,3,4,5,6,7,8,9,10,11,12,13],"label":["Antwerp","Haarlem","Dordrecht","Venice","Lisse","Het Vlie","Hamburg","Emden","Amsterdam","Delft","The Hague","Middelburg","Bremen"],"x":[-0.260697908934548,0.0882815682387856,0.548603455327459,0.38100881769269,-1,0.915541894056168,1,0.584525095268188,0.223272632971605,-0.533018752586351,-0.0548993325331134,-0.301946842460941,0.510905825603435],"y":[-0.637799107815882,-0.427468457459256,-0.531788196516244,-0.934617696638542,-1,0.801102778738664,0.382023295702693,1,0.858663434698067,-0.754392977947232,-0.915588752013053,-0.263531960247024,0.419982502903282]},"edges":{"source":["Amsterdam","Antwerp","Antwerp","Antwerp","Antwerp","Dordrecht","Emden","Haarlem","Haarlem","Haarlem","Haarlem","Hamburg","Het Vlie","Lisse","Venice"],"destination":["Bremen","Delft","Haarlem","Middelburg","The Hague","Haarlem","Bremen","Bremen","Delft","Middelburg","The Hague","Bremen","Bremen","Delft","Haarlem"],"weight":[1,68,5,1,2,1,1,2,26,1,1,1,1,1,2],"from":[9,1,1,1,1,3,8,2,2,2,2,7,6,5,4],"to":[13,10,2,12,11,2,13,13,10,12,11,13,13,10,2],"width":[1.2,14.6,2,1.2,1.4,1.2,1.2,1.4,6.2,1.2,1.2,1.2,1.2,1.2,1.4]},"nodesToDataframe":true,"edgesToDataframe":true,"options":{"width":"100%","height":"100%","nodes":{"shape":"dot","physics":false},"manipulation":{"enabled":false},"edges":{"smooth":false,"arrows":"middle"},"physics":{"stabilization":false}},"groups":null,"width":null,"height":null,"idselection":{"enabled":false},"byselection":{"enabled":false},"main":null,"submain":null,"footer":null,"background":"rgba(0, 0, 0, 0)","igraphlayout":{"type":"square"}},"evals":[],"jsHooks":[]}</script>

---

# Interaktivne vizualizacije III

```r
options(htmltools.preserve.raw = FALSE) 
library(networkD3)
nodes_d3 <- mutate(nodes, id = id - 1)
edges_d3 <- mutate(edges, from = from - 1, to = to - 1)
forceNetwork(Links = edges_d3, Nodes = nodes_d3, Source = "from", Target = "to", 
             NodeID = "label", Group = "id", Value = "weight", 
             opacity = 1, fontSize = 16, zoom = TRUE)
```

<div id="htmlwidget-c9577743cc76987a57cc" style="width:2100px;height:900px;" class="forceNetwork html-widget"></div>
<script type="application/json" data-for="htmlwidget-c9577743cc76987a57cc">{"x":{"links":{"source":[8,0,0,0,0,2,7,1,1,1,1,6,5,4,3],"target":[12,9,1,11,10,1,12,12,9,11,10,12,12,9,1],"value":[1,68,5,1,2,1,1,2,26,1,1,1,1,1,2],"colour":["#666","#666","#666","#666","#666","#666","#666","#666","#666","#666","#666","#666","#666","#666","#666"]},"nodes":{"name":["Antwerp","Haarlem","Dordrecht","Venice","Lisse","Het Vlie","Hamburg","Emden","Amsterdam","Delft","The Hague","Middelburg","Bremen"],"group":[0,1,2,3,4,5,6,7,8,9,10,11,12]},"options":{"NodeID":"label","Group":"id","colourScale":"d3.scaleOrdinal(d3.schemeCategory20);","fontSize":16,"fontFamily":"serif","clickTextSize":40,"linkDistance":50,"linkWidth":"function(d) { return Math.sqrt(d.value); }","charge":-30,"opacity":1,"zoom":true,"legend":false,"arrows":false,"nodesize":false,"radiusCalculation":" Math.sqrt(d.nodesize)+6","bounded":false,"opacityNoHover":0,"clickAction":null}},"evals":[],"jsHooks":[]}</script>

---

# Interaktivne vizualizacije IV

```r
options(htmltools.preserve.raw = FALSE) 
sankeyNetwork(Links = edges_d3, Nodes = nodes_d3, Source = "from", Target = "to", 
              NodeID = "label", Value = "weight", fontSize = 16, unit = "Letter(s)")
```

<div id="htmlwidget-b01e6b568b7befa5dc05" style="width:2100px;height:600px;" class="sankeyNetwork html-widget"></div>
<script type="application/json" data-for="htmlwidget-b01e6b568b7befa5dc05">{"x":{"links":{"source":[8,0,0,0,0,2,7,1,1,1,1,6,5,4,3],"target":[12,9,1,11,10,1,12,12,9,11,10,12,12,9,1],"value":[1,68,5,1,2,1,1,2,26,1,1,1,1,1,2]},"nodes":{"name":["Antwerp","Haarlem","Dordrecht","Venice","Lisse","Het Vlie","Hamburg","Emden","Amsterdam","Delft","The Hague","Middelburg","Bremen"],"group":["Antwerp","Haarlem","Dordrecht","Venice","Lisse","Het Vlie","Hamburg","Emden","Amsterdam","Delft","The Hague","Middelburg","Bremen"]},"options":{"NodeID":"label","NodeGroup":"label","LinkGroup":null,"colourScale":"d3.scaleOrdinal(d3.schemeCategory20);","fontSize":16,"fontFamily":null,"nodeWidth":15,"nodePadding":10,"units":"Letter(s)","margin":{"top":null,"right":null,"bottom":null,"left":null},"iterations":32,"sinksRight":true}},"evals":[],"jsHooks":[]}</script>

---

# PRAKTIČNI PRIMJER (NETWORK ANALIZA)

(Primjer terorističke mreže)

---
  
# Snaga slabih veza
<br>
<br>

.footnote[[*] Rad M.S. Granovetter-a na [poveznici](http://snap.stanford.edu/class/cs224w-readings/granovetter73weakties.pdf).]

---
  
# Slabe veze
<br>
<br>
<img src="../Foto/net3.png" width="500px" style="display: block; margin: auto;" />

---
  
# Snažne veze
<br>
<br>  
<img src="../Foto/net4.png" width="500px" style="display: block; margin: auto;" />

---

# Teroristički napad u Madridu 2004
<br>
<img src="../Foto/madrid.jpg" width="500px" style="display: block; margin: auto;" />

.footnote[ [*] Vidi rad od Jose A. Rodriguez na [poveznici](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.98.4408&rep=rep1&type=pdf)! ]

---

# Podatci
<br>

```r
# Učitaj podatke
terrorists <- read_csv("../Podatci/names.csv") 
# Pogledaj podatke
head(terrorists,5)
```

```
## # A tibble: 5 x 1
##   name           
##   <chr>          
## 1 Jamal Zougam   
## 2 Mohamed Bekkali
## 3 Mohamed Chaoui 
## 4 Vinay Kholy    
## 5 Suresh Kumar
```

---

# Podatci
<br>

```r
# Učitaj podatke
ties <- read_csv("../Podatci/edges.csv")
# Pogledaj podatke
head(ties,5)
```

```
## # A tibble: 5 x 3
##       x     y weight
##   <dbl> <dbl>  <dbl>
## 1     1     2      1
## 2     1     3      3
## 3     1     4      1
## 4     1     5      1
## 5     1     6      1
```

---

# Podatci

```r
# Prilagodi podatke
terrorists = mutate(terrorists, id = 1:nrow(terrorists)) %>% select(id, everything())
# Napravi mrežu
g = graph_from_data_frame(ties, directed = FALSE, vertices = tibble(1:nrow(terrorists)))
g # Pregled mreže
```

```
## IGRAPH 75ff9a7 UNW- 70 243 -- 
## + attr: name (v/c), weight (e/n)
## + edges from 75ff9a7 (vertex names):
##   [1] 1--2  1--3  1--4  1--5  1--6  1--7  1--8  1--9  1--11 1--12 1--13 1--14
##  [13] 1--15 1--16 1--18 1--19 1--24 1--25 1--28 1--30 1--31 1--33 1--40 1--41
##  [25] 1--44 1--50 1--57 1--58 1--61 2--3  3--4  3--5  3--7  3--8  3--9  3--11
##  [37] 3--12 3--13 3--14 3--15 3--16 3--18 3--19 3--24 3--25 3--28 3--30 3--31
##  [49] 3--33 3--40 3--41 3--44 3--57 3--58 3--61 4--5  4--19 4--24 4--28 4--30
##  [61] 4--31 4--33 4--41 5--19 5--24 5--28 5--30 5--31 5--33 5--41 6--19 6--20
##  [73] 6--39 6--40 6--44 6--54 7--8  7--10 7--11 7--12 7--13 7--14 7--15 7--16
##  [85] 7--18 7--30 7--40 7--41 7--44 7--50 7--53 7--56 7--57 7--58 7--59 7--61
## + ... omitted several edges
```

---

# Podatci
<br>
<br>

```r
# Pregledaj čvorove
V(g)
```

```
## + 70/70 vertices, named, from 75ff9a7:
##  [1] 1  2  3  4  5  6  7  8  9  10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [26] 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
## [51] 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
```

```r
vcount(g) # Broj čvorova
```

```
## [1] 70
```
---

# Podatci

```r
# Pregledaj poveznice
E(g)
```

```
## + 243/243 edges from 75ff9a7 (vertex names):
##   [1] 1 --2  1 --3  1 --4  1 --5  1 --6  1 --7  1 --8  1 --9  1 --11 1 --12
##  [11] 1 --13 1 --14 1 --15 1 --16 1 --18 1 --19 1 --24 1 --25 1 --28 1 --30
##  [21] 1 --31 1 --33 1 --40 1 --41 1 --44 1 --50 1 --57 1 --58 1 --61 2 --3 
##  [31] 3 --4  3 --5  3 --7  3 --8  3 --9  3 --11 3 --12 3 --13 3 --14 3 --15
##  [41] 3 --16 3 --18 3 --19 3 --24 3 --25 3 --28 3 --30 3 --31 3 --33 3 --40
##  [51] 3 --41 3 --44 3 --57 3 --58 3 --61 4 --5  4 --19 4 --24 4 --28 4 --30
##  [61] 4 --31 4 --33 4 --41 5 --19 5 --24 5 --28 5 --30 5 --31 5 --33 5 --41
##  [71] 6 --19 6 --20 6 --39 6 --40 6 --44 6 --54 7 --8  7 --10 7 --11 7 --12
##  [81] 7 --13 7 --14 7 --15 7 --16 7 --18 7 --30 7 --40 7 --41 7 --44 7 --50
##  [91] 7 --53 7 --56 7 --57 7 --58 7 --59 7 --61 8 --9  8 --10 8 --25 9 --25
## + ... omitted several edges
```

```r
ecount(g) # Broj poveznica
```

```
## [1] 243
```

---

# Podatci

```r
# Doddaj naziv
g$name <- "Madrid network"
g$name
```

```
## [1] "Madrid network"
```

```r
g
```

```
## IGRAPH 75ff9a7 UNW- 70 243 -- Madrid network
## + attr: name (g/c), name (v/c), weight (e/n)
## + edges from 75ff9a7 (vertex names):
##   [1] 1--2  1--3  1--4  1--5  1--6  1--7  1--8  1--9  1--11 1--12 1--13 1--14
##  [13] 1--15 1--16 1--18 1--19 1--24 1--25 1--28 1--30 1--31 1--33 1--40 1--41
##  [25] 1--44 1--50 1--57 1--58 1--61 2--3  3--4  3--5  3--7  3--8  3--9  3--11
##  [37] 3--12 3--13 3--14 3--15 3--16 3--18 3--19 3--24 3--25 3--28 3--30 3--31
##  [49] 3--33 3--40 3--41 3--44 3--57 3--58 3--61 4--5  4--19 4--24 4--28 4--30
##  [61] 4--31 4--33 4--41 5--19 5--24 5--28 5--30 5--31 5--33 5--41 6--19 6--20
##  [73] 6--39 6--40 6--44 6--54 7--8  7--10 7--11 7--12 7--13 7--14 7--15 7--16
##  [85] 7--18 7--30 7--40 7--41 7--44 7--50 7--53 7--56 7--57 7--58 7--59 7--61
## + ... omitted several edges
```

---

# Podatci
<br>
<br>

```r
E(g)$weight # Pogledaj težinu čvorova
```

```
##   [1] 1 3 1 1 1 4 1 1 4 1 1 2 2 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 3 1 1 2 1
##  [38] 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
##  [75] 1 1 1 1 3 1 1 1 2 2 3 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 1 2 1 2 1 1 1 1 1
## [112] 1 1 1 2 1 1 1 1 1 1 1 2 2 1 1 3 2 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [223] 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
```

---

# Vizualiziraj mrežu

```r
ggraph(g, layout = "with_kk") +
geom_edge_link(aes(alpha = weight)) +
geom_node_point()
```

---

# Mjere centraliteta
<br>
<br>
- Koji su najvažniji čvorovi u mreži?
<br>
- npr. najbitnije web stranice o odrđenoj temi,utjecajni akademski članci ili knjige, tajna društva (masoni)
<br>
- stupanj, težina, međusobnost

---

# Izračunaj stupanj čvorova
<br>
<br>

```r
degree(g)
```

```
##  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 
## 29  2 27 10 10  7 22  6  4  2 18 10 10 10 11 11  0 16 15  6  8  5  3 16  8  0 
## 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 
##  4 11  0 12 14  3 12  5  5  5  5  4  2 11 17  1  1 10  1  0  0  0  1  4  1  1 
## 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 
##  1  2  4  6  8 10  2  2 13  1 11  6  6  6  6  2  2  2
```

---

# Izračunaj snagu čvorova
<br>
<br>

```r
strength(g)
```

```
##  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 
## 43  2 34 10 10  7 35  7  4  3 27 10 12 14 19 17  0 21 15  6  8  5  3 16  8  0 
## 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 
##  4 11  0 12 14  3 12  5  5  5  5  4  2 12 19  1  1 10  1  0  0  0  1  4  1  1 
## 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 
##  1  2  5  7  9 11  2  2 14  1 11  6  6  6  6  2  2  2
```

---

# Međusobnost (betweenness)

---

# Vizualizacija međusobnosti

```r
dist_weight = 1 / E(g)$weight
g$betweenness <- edge_betweenness(g, weights = dist_weight)

ggraph(g, layout = "with_kk") +
  geom_edge_link(aes(alpha = g$betweenness)) +
  geom_node_point()
```

---

# Najpovezaniji teroristi I

```r
terrorists  <- terrorists %>%
  mutate(degree = degree(g),
           strength = strength(g))

arrange(terrorists, desc(degree))
```

```
## # A tibble: 70 x 4
##       id name               degree strength
##    <int> <chr>               <dbl>    <dbl>
##  1     1 Jamal Zougam           29       43
##  2     3 Mohamed Chaoui         27       34
##  3     7 Imad Eddin Barakat     22       35
##  4    11 Amer Azizi             18       27
##  5    41 Said Berrak            17       19
##  6    18 Galeb Kalaje           16       21
##  7    24 Naima Oulad Akcha      16       16
##  8    19 Abderrahim Zbakh       15       15
##  9    31 Jamal Ahmidan          14       14
## 10    61 Mohamed El Egipcio     13       14
## # ... with 60 more rows
```

---

# Najpovezaniji teroristi II

```r
arrange(terrorists, desc(strength))
```

```
## # A tibble: 70 x 4
##       id name               degree strength
##    <int> <chr>               <dbl>    <dbl>
##  1     1 Jamal Zougam           29       43
##  2     7 Imad Eddin Barakat     22       35
##  3     3 Mohamed Chaoui         27       34
##  4    11 Amer Azizi             18       27
##  5    18 Galeb Kalaje           16       21
##  6    15 Mohamed Belfatmi       11       19
##  7    41 Said Berrak            17       19
##  8    16 Said Bahaji            11       17
##  9    24 Naima Oulad Akcha      16       16
## 10    19 Abderrahim Zbakh       15       15
## # ... with 60 more rows
```

---

# Izolirani teroristi

```r
filter(terrorists,degree == 0)
```

```
## # A tibble: 6 x 4
##      id name                      degree strength
##   <int> <chr>                      <dbl>    <dbl>
## 1    17 "Al\xed Amrous"                0        0
## 2    26 "Abdelhalak Bentasser"         0        0
## 3    29 "Faisal Alluch"                0        0
## 4    46 "Mohamad Bard Ddin Akkab"      0        0
## 5    47 "Abu Zubaidah"                 0        0
## 6    48 "Sanel Sjekirika"              0        0
```

---

# Slični parovi terorista

```r
ties <- ties %>% rename(from = x, to = y) # prilagodi nazive
ggplot(ties, aes(x = from, y = to, color = as.factor(weight))) +
  geom_point() +
  labs(color = "weigth")
```

---

# Slični parovi terorista

```r
# Dodaj recipročne veze
ties2 = mutate(ties, temp = to, to = from, from = temp) %>% select(-temp)
ties2 = rbind(ties, ties2)
ggplot(ties2, aes(x = from, y = to, color = as.factor(weight))) +
  geom_point() +
  labs(color = "weigth")
```

---

# Slični parovi terorista

```r
##Pripremi podatke##
# Ukloni izolirane teroriste
isolated = filter(terrorists, degree == 0)$id
g = delete_vertices(g, isolated)
# Napravi adjecany matricu
A = as_adjacency_matrix(g, attr = "weight", sparse = FALSE)
# Sličnost kao Pearsonova korelacija
S = cor(A)
# Ukloni sličnost sa samim sobom
S = S + diag(-1, nrow(A))
# Deskriptiva
summary(c(S))
```

```
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## -0.27574 -0.07729 -0.03336  0.07074  0.17037  1.00000
```

---

# Slični parovi terorista

```r
# Napravi adjecancy matricu
h <- graph_from_adjacency_matrix(S, mode = "undirected", weighted = TRUE)
# Pretvori u data.frame(tibble)
sim = as.tibble(as_data_frame(h, what = "edges")) %>% 
   mutate(from = as.integer(from), to = as.integer(to)) %>%
   arrange(desc(weight))
# join sa podatkovnim skupom terrorists
sim_joint <- sim %>% 
 left_join(terrorists, c("from" = "id")) %>% 
  left_join(terrorists, c("to" = "id")) %>%
  filter(degree.x >= 10, degree.y >= 10) %>%
  select(-strength.x, -strength.y)
```

---

# Najsličniji parovi
<br>

```r
head(sim_joint)
```

```
## # A tibble: 6 x 7
##    from    to weight name.x              degree.x name.y           degree.y
##   <int> <int>  <dbl> <chr>                  <dbl> <chr>               <dbl>
## 1    13    14  0.906 Mohamed Atta              10 Ramzi Binalshibh       10
## 2     4     5  0.881 Vinay Kholy               10 Suresh Kumar           10
## 3    12    58  0.855 Abu Musad Alsakaoui       10 Shakur                 10
## 4    12    13  0.847 Abu Musad Alsakaoui       10 Mohamed Atta           10
## 5    12    15  0.836 Abu Musad Alsakaoui       10 Mohamed Belfatmi       11
## 6     4    28  0.831 Vinay Kholy               10 Basel Ghayoun          11
```

---

# Najmanje slični parovi
<br>

```r
tail(sim_joint)
```

```
## # A tibble: 6 x 7
##    from    to weight name.x              degree.x name.y          degree.y
##   <int> <int>  <dbl> <chr>                  <dbl> <chr>              <dbl>
## 1    16    63 -0.188 Said Bahaji               11 Semaan Gaby Eid       11
## 2     1    63 -0.194 Jamal Zougam              29 Semaan Gaby Eid       11
## 3    12    63 -0.196 Abu Musad Alsakaoui       10 Semaan Gaby Eid       11
## 4    40    63 -0.199 Abdeluahid Berrak         11 Semaan Gaby Eid       11
## 5     3    63 -0.219 Mohamed Chaoui            27 Semaan Gaby Eid       11
## 6     7    63 -0.226 Imad Eddin Barakat        22 Semaan Gaby Eid       11
```

---

# Vizualiziraj sličnost

```r
h2 <- graph_from_data_frame(filter(sim_joint, weight >= 0.60), directed = FALSE, vertices = terrorists)
h2 <- delete_vertices(h2, which(degree(h2) == 0))

ggraph(h2) + 
  geom_edge_link(aes(alpha = weight)) + 
  geom_node_point() + 
  theme_graph()
```

---

# Vizualiziraj sličnost

```r
# Dodaj snagu čvorova
ggraph(h2) + 
  geom_edge_link(aes(alpha = weight)) + 
  geom_node_point(aes(size = strength)) +
  theme_graph()
```

<img src="10_NET_files/figure-html/unnamed-chunk-63-1.png" style="display: block; margin: auto;" />
---

# Vizualiziraj sličnost

```r
# Dodaj nazive čvorova
ggraph(h2) + 
  geom_edge_link(aes(alpha = weight)) + 
  geom_node_point() +
  geom_node_text(aes(label = name), repel=T) +
  theme_graph()
```

---

# Vizualiziraj sličnost

```r
V(h2)$betw = betweenness(h2) # dodaj međusobnost u mrežu

ggraph(h2) + 
  geom_edge_link(aes(alpha = weight)) + 
  geom_node_point(aes(size = betw)) +
  theme_graph()
```

---

# Hvala na pažnji

(Zadnje predavanje!)