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Network Analysis and Visualization with R and igraph Katherine Ognyanova, www.kateto.net NetSciX 2016 School of Code Workshop, Wroclaw, Poland Contents 1. A quick reminder of R basics 3 3 1.1 Assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Value comparisons 4 1.3 Special constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Vectors 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Factors 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Matrces & Arrays 8 1.7 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.8 Data Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.9 Flow Control and loops 1.10 R plots and colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.11 R troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2. Networks in igraph 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1 Create networks 2.2 Edge, vertex, and network attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 21 2.3 Speciﬁc graphs and graph models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Reading network data from ﬁles 3.1 DATASET 1: edgelist 3.2 DATASET 2: matrix 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4. Turning networks into igraph objects 28 4.1 Dataset 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.2 Dataset 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1

5. Plotting networks with igraph 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.1 Plotting parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.2 Network layouts 5.3 Improving network plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.4 Interactive plotting with tkplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.5 Other ways to represent a network 5.6 Plotting two-mode networks with igraph . . . . . . . . . . . . . . . . . . . . . . . . . . 48 6. Network and node descriptives 50 6.1 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6.2 Reciprocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6.3 Transitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6.4 Diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.5 Node degrees 6.6 Degree distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.7 Centrality & centralization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.8 Hubs and authorities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 7. Distances and paths 56 8. Subgroups and communities 59 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 8.1 Cliques 8.2 Community detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 8.3 K-core decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 9. Assortativity and Homophily 64 2

Note: You can download all workshop materials here, or visit kateto.net/netscix2016. This tutorial covers basics of network analysis and visualization with the R package igraph (main- tained by Gabor Csardi and Tamas Nepusz). The igraph library provides versatile options for descriptive network analysis and visualization in R, Python, and C/C++. This workshop will focus on the R implementation. You will need an R installation, and RStudio. You should also install the latest version of igraph for R: install.packages("igraph") 1. A quick reminder of R basics Before we start working with networks, we will go through a quick introduction/reminder of some simple tasks and principles in R. 1.1 Assignment You can assign a value to an object using assign(), <-, or =. x <- 3 x y <- 4 y + 5 # Assignment # Evaluate the expression and print result # Assignment # Evaluation, y remains 4 z <- x + 17*y # Assignment # Evaluation z 3

rm(z) z # Remove z: deletes the object. # Error! 1.2 Value comparisons We can use the standard operators <, >, <=, >=, ==(equality) and != (inequality). Comparisons return Boolean values: TRUE or FALSE (often abbreviated to just T and F). # Equality # Inequality 2==2 2!=2 x <= y # less than or equal: "<", ">", and ">=" also work 1.3 Special constants Special constants include: • NA for missing or undeﬁned data • NULL for empty object (e.g. null/empty lists) • Inf and -Inf for positive and negative inﬁnity • NaN for results that cannot be reasonably deﬁned # NA - missing or undefined data 5 + NA is.na(5+NA) # Check if missing # When used in an expression, the result is generally NA # NULL - an empty object, e.g. a null/empty list 10 + NULL is.null(NULL) # check if NULL # use returns an empty object (length zero) Inf and -Inf represent positive and negative inﬁnity. They can be returned by mathematical operations like division of a number by zero: 5/0 is.finite(5/0) # Check if a number is finite (it is not). NaN (Not a Number) - the result of an operation that cannot be reasonably deﬁned, such as dividing zero by zero. 0/0 is.nan(0/0) 1.4 Vectors Vectors can be constructed by combining their elements with the important R function c(). 4

v1 <- c(1, 5, 11, 33) v2 <- c("hello","world") v3 <- c(TRUE, TRUE, FALSE) # Logical vector, same as c(T, T, F) # Numeric vector, length 4 # Character vector, length 2 (a vector of strings) Combining diﬀerent types of elements in one vector will coerce the elements to the least restrictive type: v4 <- c(v1,v2,v3,"boo") # All elements turn into strings Other ways to create vectors include: # same as c(1,2,3,4,5,6,7) v <- 1:7 v <- rep(0, 77) # repeat zero 77 times: v is a vector of 77 zeroes v <- rep(1:3, times=2) # Repeat 1,2,3 twice v <- rep(1:10, each=2) # Repeat each element twice v <- seq(10,20,2) # sequence: numbers between 10 and 20, in jumps of 2 v1 <- 1:5 v2 <- rep(1,5) # 1,2,3,4,5 # 1,1,1,1,1 Check the length of a vector: length(v1) length(v2) Element-wise operations: v1 + v2 v1 + 1 v1 * 2 v1 + c(1,7) # This doesnt work: (1,7) is a vector of different length # Element-wise addition # Add 1 to each element # Multiply each element by 2 Mathematical operations: sum(v1) mean(v1) sd(v1) cor(v1,v1*5) # Correlation between v1 and v1*5 # The sum of all elements # The average of all elements # The standard deviation Logical operations: v1 > 2 v1==v2 v1!=v2 (v1>2) | (v2>0) (v1>2) & (v2>0) (v1>2) || (v2>0) (v1>2) && (v2>0) # Each element is compared to 2, returns logical vector # Are corresponding elements equivalent, returns logical vector. # Are corresponding elements *not* equivalent? Same as !(v1==v2) # | is the boolean OR, returns a vector. # & is the boolean AND, returns a vector. # || is the boolean OR, returns a single value # && is the boolean AND, ditto 5

Vector elements: v1[3] v1[2:4] v1[c(1,3)] v1[c(T,T,F,F,F)] v1[v1>3] # third element of v1 # elements 2, 3, 4 of v1 # elements 1 and 3 - note that your indexes are a vector # elements 1 and 2 - only the ones that are TRUE # v1>3 is a logical vector TRUE for elements >3 Note that the indexing in R starts from 1, a fact known to confuse and upset people used to languages that index from 0. To add more elements to a vector, simply assign them values. v1[6:10] <- 6:10 We can also directly assign the vector a length: length(v1) <- 15 # the last 5 elements are added as missing data: NA 1.5 Factors Factors are used to store categorical data. #vector eye.col.v <- c("brown", "green", "brown", "blue", "blue", "blue") eye.col.f <- factor(c("brown", "green", "brown", "blue", "blue", "blue")) #factor eye.col.v ## [1] "brown" "green" "brown" "blue" "blue" "blue" eye.col.f ## [1] brown green brown blue blue ## Levels: blue brown green blue R will identify the diﬀerent levels of the factor - e.g. all distinct values. The data is stored internally as integers - each number corresponding to a factor level. levels(eye.col.f) # The levels (distinct values) of the factor (categorical var) ## [1] "blue" "brown" "green" as.numeric(eye.col.f) # As numeric values: 1 is blue, 2 is brown, 3 is green ## [1] 2 3 2 1 1 1 6

as.numeric(eye.col.v) # The character vector can not be coerced to numeric ## Warning: NAs introduced by coercion ## [1] NA NA NA NA NA NA as.character(eye.col.f) ## [1] "brown" "green" "brown" "blue" "blue" "blue" as.character(eye.col.v) ## [1] "brown" "green" "brown" "blue" "blue" "blue" 1.6 Matrces & Arrays A matrix is a vector with dimensions: m <- rep(1, 20) dim(m) <- c(5,4) # A vector of 20 elements, all 1 # Dimensions set to 5 & 4, so m is now a 5x4 matrix Creating a matrix using matrix(): m <- matrix(data=1, nrow=5, ncol=4) # same matrix as above, 5x4, full of 1s m <- matrix(1,5,4) dim(m) # What are the dimensions of m? # same matrix as above ## [1] 5 4 Creating a matrix by combining vectors: m <- cbind(1:5, 5:1, 5:9) # Bind 3 vectors as columns, 5x3 matrix m <- rbind(1:5, 5:1, 5:9) # Bind 3 vectors as rows, 3x5 matrix Selecting matrix elements: m <- matrix(1:10,10,10) # The whole second row of m as a vector # The whole second column of m as a vector m[2,3] # Matrix m, row 2, column 3 - a single cell m[2,] m[,2] m[1:2,4:6] # submatrix: rows 1 and 2, columns 4, 5 and 6 m[-1,] # all rows *except* the first one Other operations with matrices: 7

# Are elements in row 1 equivalent to corresponding elements from column 1: m[1,]==m[,1] # A logical matrix: TRUE for m elements >3, FALSE otherwise: m>3 # Selects only TRUE elements - that is ones greater than 3: m[m>3] t(m) m <- t(m) m %*% t(m) m * m # Transpose m # Assign m the transposed m # %*% does matrix multiplication # * does element-wise multiplication Arrays are used when we have more than 2 dimensions. We can create them using the array() function: a <- array(data=1:18,dim=c(3,3,2)) # 3d with dimensions 3x3x2 a <- array(1:18,c(3,3,2)) # the same array 1.7 Lists Lists are collections of objects. A single list can contain all kinds of elements - character strings, numeric vectors, matrices, other lists, and so on. The elements of lists are often named for easier access. l1 <- list(boo=v1,foo=v2,moo=v3,zoo="Animals!") # A list with four components l2 <- list(v1,v2,v3,"Animals!") Create an empty list: l3 <- list() l4 <- NULL Accessing list elements: # Access boo with single brackets: this returns a list. l1["boo"] l1[["boo"]] # Access boo with double brackets: this returns the numeric vector l1[[1]] l1$boo # Returns the first component of the list, equivalent to above. # Named elements can be accessed with the $ operator, as with [[]] Adding more elements to a list: l3[[1]] <- 11 # add an element to the empty list l3 l4[[3]] <- c(22, 23) # add a vector as element 3 in the empty list l4. Since we added element 3 to the list l4above, elements 1 and 2 will be generated and empty (NULL). 8

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