Network Analysis

DA 101, Dr. Ladd

Week 12

What are Networks?

Networks are made up of…

Entities (entity = node/vertex/actor)
Relationships (relationship = edge/link/tie)
We’ll use “nodes” and “edges”

Nodes and Edges have Attributes

Node Attributes

numerical (size)
categorical (color)

Edge Attributes

Directed and Undirected Edges

Weighted and Unweighted Edges

Edge Types

Multiple Edges “in a row” Make a Path

Path & Diameter

(& Average Shortest Path Length)

Some special kinds of nodes

Isolates

Hubs

Bridges

Measuring a node’s “importance” with centrality

Degree

Strength

Betweenness

Different kinds of entities or nodes

Unipartite/unimodal

Bipartite/bimodal

Bipartite (cont.)

Multipartite/k-partite/multimodal

Groups of nodes within a network

Connected components

Cliques and clustering

Clustering Coefficient

Communities and community detection

Density

A Sparse Network

A Dense Network

There are many ways to visualize a network

Adjacency Matrix

Adjacency List

A adjacent to B,C
B adjacent to A,C
C adjacent to A,B

Node-Link Diagram

Other Important Concepts

Triadic Closure

Assortative mixing/Homophily

Preferential Attachment

Weak Ties

Small World Network

low average path length
low clustering coefficients
degree distribution follows power law (a few large hubs)
low diameter (usually around “six degrees”)

Working with Networks in R

Let’s start with an example.

We’ll need two new libraries.

library(igraph) # Network tools and metrics

library(networkD3) # Interactive network visualizations

We can download the data and load it into a “network object” with iGraph.

First, download got-edges.csv. What does this data look like?

# Read in edgelist CSV
edges <- read_csv("got-edges.csv")

# Create igraph object from edgelist
G <- graph_from_data_frame(d = edges, directed = FALSE)
E(G)$weight <- E(G)$Weight #Make sure weight is labeled correctly

Let’s make two versions of a node-link diagram.

# The default R version
plot(G)

# A better D3 version
simpleNetwork(edges, opacity=1, zoom=TRUE)

We can use iGraph to calculate different metrics.

# Calculate degree and add to network data
V(G)$degree <- degree(G)

# Calculate betweenness centrality and add to network data
V(G)$betweenness <- betweenness(G, normalized=TRUE)

# Calculate the ratio of betweenness to degree
# (i.e. This is the node that functions most as a "bridge")
V(G)$betweenness_over_degree <- betweenness(G)/degree(G)

You can convert node/vertex data to a dataframe.

nodes <- igraph::as_data_frame(G, what="vertices")

What happens if you try:

edges <- igraph::as_data_frame(G, what="edges")

With a dataframe, you can easily see degree and betweenness distributions.

# Degree distribution
ggplot(nodes, aes(degree)) +
     geom_histogram()

How would you make a graph of the betweenness distribution?

Finally, let’s make a better node-link diagram.

# Convert data to networkD3-friendly format & calculate modularity clusters
G_d3 <- igraph_to_networkD3(G, membership(cluster_fast_greedy(G)))

# Add degree to node data and weight to link data
G_d3$nodes$degree <- V(G)$degree
G_d3$links$weight <- E(G)$weight

# Create force network with nodes sized by degree and colored by modularity
forceNetwork(Links=G_d3$links, Nodes = G_d3$nodes,
             Source = 'source', Target = 'target',
             Value= 'weight', NodeID = 'name',
             Group = 'group', Nodesize='degree',
             zoom = TRUE, opacity = 1)