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# «NETWORKING IN EVERYDAY LIFE by Bernard J. Hogan A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy ...»

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So, I would quickly check my email—quickly check my inbox if I knew I’d have to ﬁre something off to someone...so, it’s really for very brief periods of time that I’m on the computer with the kids around because it’s just not conducive to getting any serious work done. So, you know, they’ll come— he’ll come and try and hit the keys. He’ll elbow himself into that little space and you know try and get in there and so, you know...it’s a very, very brief period of time that I even bother trying.

One thing that stands out from these networks is that family are generally connected as one component or two (when there are in-laws). Second, friends may be connected or fragmented, often depending on the perspective of the individual and the sort of activities they engage in. Neighbours are almost always disconnected while organization members are almost always embedded in larger groups. However, these insights are merely anecdotal at this point. Below, I offer a more broad series of metrics about the networks that should clarify these intuitions quantitatively.

To examine the relationship between role and links quantitatively, I employ a mixing matrix. Each row and column represents a category (such as male and female).

Each cell represents the percentage of links that go from the row category to the column category. For example, if one looks at mixing in telephone conversations by gender, then the diagonals of the matrix are the percentage of conversations that are male-male and female-female. The off-diagonals represent the percentage of calls that are from males to females, and from females to males. If it is a directed network, both the top and bottom half of the matrix is ﬁlled out. If it is an undirected network, as is the case in this research, only half of the matrix is ﬁlled out.

While not common in social network analysis, mixing matrices have been used to assess patterns of diffusion in sexually transmitted infection (STI) research (Gupta, Anderson, and May, 1989). If people infected with STIs have repeated sex with others

## CHAPTER 6. WITHIN-NETWORK VARIATIONS AND NETWORKED INDIVIDUALISM 143

who have STIs then the particular infection is considered very infectious. However, if there are many links between STI-positive individuals and STI-negative individuals then the strain is not as infectious. This work was subsequently generalized by Newman (2003) who demonstrated both continuous and categorial mixing in many domains, such as address books, the Internet server structure and neural networks.

For example, the Internet backbone is highly assorted with servers of very high degree connecting to local computers of very low degree.

Once a mixing matrix is calculated, past researchers have then reduced this matrix to a single value by calculating the proportion of the ties on the diagonal (ties between alters of like type) to those on the off diagonal (ties between those of different types). This value is called assortativity, or the assortative mixing coefﬁcient(2003).

My analysis will pursue a different route. This is because I am not as interested in the per-network level of mixing as I am interested in the per-role level of mixing. Also, assortative mixing values are intended for connected networks, whereas most personal networks contain numerous disconnected components. So instead of calculating a single value for each of the 86 networks, I calculate the average mixing value for each type across all networks (for example, the average number of links between family members across all networks, or the average number of links between neighbours and workmates).

The average mixing scores are presented in Table 6.3.2. It is an undirected network so only one half of the matrix is shown. Each cell in the matrix holds two values.

The top value is the weighted average whereas the bottom value is the unweighted average. The weighted average represents the percentage of ties between alters of like type averaged across all networks, whereas the bottom value is the percentage of ties between alters of like type as a total of all ties from all networks (i.e., it is the dyadic mixing regardless of how such links are distributed through the networks). I present both of these values since the difference between them gives some clues as to whether

## CHAPTER 6. WITHIN-NETWORK VARIATIONS AND NETWORKED INDIVIDUALISM 144

–  –  –

Table 6.1: Mixing matrix of links within networks and between dyads by role The top number is the percentage of links between roles averaged across all networks (the weighted value).

The bottom is the percentage averaged across all dyads (the unweighted value).

## CHAPTER 6. WITHIN-NETWORK VARIATIONS AND NETWORKED INDIVIDUALISM 145

these linking patterns are the result of especially large or especially small networks.

As a ﬁctitious example consider the following: Four networks have a total of 100 links. Of these, 40 links are between family members, but they are unequally distributed. If one network has 10 ties between family members out of 40 ties (25 percent) while the remaining three networks each have 10 ties between family members out of 20 total ties (50 percent each), the weighted score will be: (.25+.50+.50.+.50)/4 for an average of 44 percent of ties. By contrast the unweighted score will be (10+10+10+10)/100 for an average of 40 percent of all dyads. Thus, smaller networks play a larger role in the weighted score. So in general, where the weighted score is larger than the unweighted, it is because smaller networks are disproportionately responsible for the links. Where the weighted score is smaller, then larger-than-average networks are disproportionately responsible.

To give a concrete example from the data, notice that the ﬁrst cell describes the links between immediate family members. The weighted average is 26.7, meaning that on average 26.7 percent of links in the networks are between immediate family members.

The unweighted average is 18.3 meaning that 18.3 percent of dyads are family-family links. The fact that the weighted average is much higher than the unweighted average indicates that smaller networks (or networks with fewer family members) are disproportionately responsible for the density of family-family links. So smaller networks count for disproportionately more in the weighted score.

The raw link percentages in the mixing matrix are interesting in their own right, but it is possible to walk away from the scores with a false sense of the relevance of the different roles. Indeed, most of the links are between family while few of the links are between organization members. However, there are also fewer organization members in the networks than there are family members. For this reason, it is more interesting to examine not merely the average mixing matrix, but the ratio of homophilous ties (of like role) to heterophilous ties (between alters of different roles). This measure

## CHAPTER 6. WITHIN-NETWORK VARIATIONS AND NETWORKED INDIVIDUALISM 146

–  –  –

Table 6.2: Ordered list of the ratio of in-links to out-links by role is more fair as this ratio is based solely on the number of links in to links out.

As such, regardless of the size difference between the number of family members and organization members, the ratio of homophilous links to heterophilous links may still be on par.

Here one can see that in general,

## CHAPTER 6. WITHIN-NETWORK VARIATIONS AND NETWORKED INDIVIDUALISM 147

immediate family members are most insular and group-like in the network. A value of 1.66 means that on average there are 1.66 links among family members for every link between family members and other roles. While 1.66 is not an especially high value, by combining the ratios for immediate family and extended family, the ratio is a very substantial 4.18, meaning that there are 4.18 links between kin (immediate and extended combined) for every link between kin and other members of the network.

At this point the reader may be inclined to wonder about those individuals with no links to others. Do they also follow the same pattern? As seen in the third data column of 6.2, they do in fact follow this general pattern and reinforce the general claim about the group-like or individualistic qualities of different roles. This column shows the percent of nodes in the network who are isolates, sorted by role. To be clear, this is the percent of a speciﬁc role who are isolates, not the percent of isolates who are a speciﬁc role. Kin are the least likely to be isolated individuals in the network, followed by organization members. Again, friends and workmates are in the middle while neighbours, ‘others’, and online friends are the most likely to be isolates.

There are (at least) two ways in which one can interpret these ratios in light of the theory of networked individualism. The ﬁrst is conceptual and the second is methodological. Conceptually speaking, those roles that have a very low in/out ratio are going to be most likely associated with networked individualistic networking practices.

These are the sparsely connected ties that bridge networks, rather than the densely connected ties that are representative of a ‘group’ structure. Returning to Table 6.2, one can see the rank order of the roles on their in/out ratios. Kin are the most likely ties to represent a group, whereas online friends are the least likely roles to represent a group (in the personal network). Also particularly interesting is the fact alters from organizations are twice as likely to link inwards as to link outwards. Thus alters from organizations can be interpreted as having a group-like structure. But counterintuitively, it also means that alters from organizations can serve the bridging function

## CHAPTER 6. WITHIN-NETWORK VARIATIONS AND NETWORKED INDIVIDUALISM 148

that has been asserted in the literature by numerous social capital scholars (Putnam, 2000; Erickson, 2001; Lai, Lin, and Leung, 1998). How can both conclusions be the case? This is a group of individuals who are linked together and thus share a common organizational order, but members of this order are drawn from separate personal networks and do not otherwise link in to these personal networks very much. Therefore, an organizational group can serve as a nexus of several personal networks. The group itself acts as a bridge between personal networks, even if the group itself is densely connected (Feld, 1982).

Interestingly, it follows from this logic that neighbours represent networked individualistic relations, although to a much lesser extent than online individuals for they are slightly more likely to link to other network members than they are to link to other neighbours. In fact, they are less insular than any other group, other than online and ‘other’, both of which are difﬁcult to categorize since they represent such a small fraction of ties overall. Online ties represent a mere 0.5 percent of all links, while ‘other’ represents a measly 2 percent of all links. Nevertheless, this ﬁnding about the linking patterns of neighbours is in conformity with Wellman’s concept that we have shifted from door-to-door neighbourhoods to person-to-person networks. It is not the case that individuals know a tightly knit group of spatially proximate individuals, but selectively choose a handful of neighbours who are linked, if at all, to non-neighbours.

–  –  –

Moreover, if I could control for the number of neighbours that are merely linked to their spouses, I am certain this number of in-links to out-links would be even lower.

Unfortunately, the data set cannot reliably facilitate such a control.

6.3.3 Part Ib: Variations in contact by role.

In addition to examining the links between network members, one can use data on contact with alters to round out our understanding of how networking varies by role.

## CHAPTER 6. WITHIN-NETWORK VARIATIONS AND NETWORKED INDIVIDUALISM 149

–  –  –

Table 6.3: Ordered list of the percent of alters contacted monthly by role This second part of the role analysis should be treated with care, however.

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