# Errata:

**Analyzing the Social Web** (1^{st} Ed.)

## Chapter 2

### Clusters

We are also interested in clusters of nodes. In Figure ~~2.6~~ 2.7, we see a group of nodes to the lower right that have many connections between them.

### Egocentric Networks

One of the most important types of subgraphs we will consider is the egocentric network. This is a network we pull out by selecting a node and all of its connections. In Figure ~~2.6~~ 2.7, node D is connected to nodes A, E, B, C, and Q. There are edges from D to each of these nodes and edges between them. When considering egocentric networks, we can choose which of those to include. ~~Consider Figure 2.7.~~

### Paths and connectedness

#### Paths

In Figure 2.7, there are ~~two~~ three shortest paths from Node F to Node E: ~~F–A–E and F–B–E~~ F–A–E, F–B–E, and F–Q–E.

### Corrected Figures

#### Adjacency Matrix (p15)

#### 2.8

## Chapter 3

### Betweenness centrality (page 30)

For example, consider ~~Figure 3.4~~ the example network in the exercises section of this chapter. Let’s compute betweenness centrality for node B. There are ~~10~~ 21 pairs of nodes to consider: ~~AC, AD, AE, AF, CD, CE, CF, DE, DF, and EF.~~ AC, AD, AE, AF, AG, AH, CD, CE, CF, CG, CH, DE, DF, DG, DH, EF, EG, EH, FG, FH, and GH. (Note that since this is an undirected network, we only consider each pair once.) Without counting, we know that 100% of the shortest paths from A to every other node in the network go through B, since A can’t reach the rest of the network without B. Thus, the fractions for ~~AC, AD, AE, and AF~~ AC, AD, AE, AF, AG, and AH are all 1.

From C to D, there are two shortest paths: one through B and one through E. Thus, 1 ÷ 2 = 0.5 go through B. ~~The same is true for the shortest path from D to C.~~ For the remaining pairs~~—CE, CF, DE, DF, and EF—~~ , no shortest paths go through B. Thus, the fraction for all of these is zero. Now we can calculate the betweenness for B:

~~4×1 (A to all others) + 0.5 (DC) + 0.5 (CD) + 14×0 (all remaining pairs) = 4 + 0.5 + 0.5 + 0 = 5~~

6×1 (A to all others) + 0.5 (CD) + 14×0 (all remaining pairs) = 6 + 0.5 + 0 = 6.5

In contrast, the betweenness centrality of A is zero, since no shortest paths between ~~D, C, D, E, and F~~ C, D, E, F, G, and H go through A.

Betweenness centrality is one of the most frequently used centrality measures. It captures how important a node is in the flow of information from one part of the network to another.

In directed networks, betweenness can have several meanings. For example, consider a Twitter account. A user with high betweenness may be followed by many others who don’t follow the same people as the user. This would indicate that the user is well-followed. Alternatively, the user may have fewer followers, but connect them to many accounts that are otherwise distant. This would indicate that the user is a reader of many people. Understanding the direction of the edges for a node is important to understand the meaning of centrality.

### Figure 3.7 (caption)

The 1.5-diameter egocentric networks for nodes A (a) and B (b) from Figure ~~3.2~~ 3.6.

### Connectivity (page 36)

Density measures the ~~percentage~~ ratio of possible edges in a graph.

### Corrected Figures

#### 3.6

#### 3.7

## Chapter 4

### Figure 4.17 (caption, page 60)

The same network of senators as shown in Figure ~~4.13~~ 4.16, now filtered to include only edges between senators who have voted the same way on at least two-thirds of bills.

## Chapter 5

### Page 70

We can form ~~three~~ four triads with P, F, and another node where there are two strong ties: PFO, PFH, PFN, and PFA.

## Chapter 8

### (page 116)

~~Because of the bias and structural differences of a sampled network created using snowball sampling, structural statistics are not useful on these graphs.~~
Structural statistics aren’t useful on networks created using snowball sampling, due to the bias and structural differences.