---
title: "oddnet"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{oddnet}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(oddnet)
library(igraph)
```

## Synthetic data
We create a sequence of temporal networks based on the Erdos Renyi construction and insert an anomaly at location 50. For this series, we make the edge probability increase from 0.01 to 0.2. 

```{r readdata}
set.seed(1)
networks <- list()
p.or.m.seq <- seq(from = 0.01, to = 0.2, length.out = 100)
p.or.m.seq[50] <- p.or.m.seq[50] + 0.2  # anomalous network
 for(i in 1:100){
  gr <- igraph::erdos.renyi.game(100, p.or.m = p.or.m.seq[i])
  networks[[i]] <- igraph::as_adjacency_matrix(gr)
}
```

Let's plot a couple of networks. 


## Plotting
```{r plotnetworks}

# Plotting
network_1 <- networks[[1]]
gr <- igraph::graph_from_adjacency_matrix(network_1)
plot(gr, 
     layout = layout_with_fr, 
     vertex.size=3, 
     vertex.label=NA,
     edge.arrow.size=0.2, 
     main = "Network 1")



network_30 <- networks[[30]]
gr <- igraph::graph_from_adjacency_matrix(network_30)
plot(gr, 
     layout = layout_with_fr, 
     vertex.size=3, 
     vertex.label=NA,
     edge.arrow.size=0.2, 
     main = "Network 30")


network_80 <- networks[[80]]
gr <- igraph::graph_from_adjacency_matrix(network_80)
plot(gr, 
     layout = layout_with_fr, 
     vertex.size=3, 
     vertex.label=NA,
     edge.arrow.size=0.2, 
     main = "Network 80")
```

The networks have increased in connectivity because the edge probability increases over time. Let's look at the anomalous network at t = 50.

```{r plotanomaly}

# Plotting
network_a <- networks[[50]]
gr <- igraph::graph_from_adjacency_matrix(network_a)
plot(gr, 
     layout = layout_with_fr, 
     vertex.size=3, 
     vertex.label=NA,
     edge.arrow.size=0.2, 
     main = "Network 50 - Anomaly")
```


## Features
Both networks at t = 50 and t = 80 look alike. Let's explore their degree distributions.

```{r degreedist}
network_80 <- networks[[80]]
gr <- igraph::graph_from_adjacency_matrix(network_80)
hist(degree(gr))

network_a <- networks[[50]]
gr <- igraph::graph_from_adjacency_matrix(network_a)
hist(degree(gr))

```

We see a clear difference in the degree distributions of the two networks. Let's look at the average degree of the network sequence.

```{r avgdeg}
avg_deg <- rep(0, 100)
max_deg <- rep(0, 100)
for(i in 1:100){
  network <- networks[[i]]
  gr <- igraph::graph_from_adjacency_matrix(network)
  avg_deg[i] <- mean(degree(gr))
  max_deg[i] <- max(degree(gr))
}
plot(avg_deg, type = "l")
plot(max_deg, type = "l")
```

We clearly see the anomaly at 50. Oddnet is a feature-based method. By computing many features it finds anomalies using time series methods. Let's find the anomalous networks using oddnet.

## Anomalies
```{r anomalous}
anomalous_networks(networks)
```

We see the correct anomaly is identified with low conditional probability.