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We’ve seen examplesof such datasets throughout these first two chapters, and it’s useful at this point to stepback and think more systematically about where people have been getting the data thatthey employ in large-scale studies of networks. Swds patch 47 48 adobe. To put this in perspective, we note first of all that there are several distinct reasonswhy you might study a particular network dataset. One is that you may care about theactual domain it comes from, so that fine-grained details of the data itself are potentiallyas interesting as the broad picture.

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An icon used to represent a menu that can be toggled by interacting with this icon. Conceptual Modeling for Data Warehouse and OLAP Applications #48. How does collaborative STEM project-based learning change when the participating students represent fundamentally distinct cultures, countries, economic, and social backgrounds, and work together o.

Chapter 4Networks in Their SurroundingContexts In Chapter 3 we considered some of the typical structures that characterize social net-works, and some of the typical processes that affect the formation of links in the network. Ourdiscussion there focused primarily on the network as an object of study in itself, relativelyindependent of the broader world in which it exists. However, the contexts in which a social network is embedded will generally have signif-icant effects on its structure, Each individual in a social network has a distinctive set ofpersonal characteristics, and similarities and compatibilities among two people’s characteris-tics can strongly influence whether a link forms between them.


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Triadic closure is intuitively very natural, and essentiallyeveryone can find examples from their own experience. Moreover, experience suggests someof the basic reasons why it operates. One reason why B and C are more likely to becomefriends, when they have a common friend A, is simply based on the opportunity for B and Cto meet: if A spends time with both B and C, then there is an increased chance that theywill end up knowing each other and potentially becoming friends. A second, related reasonis that in the process of forming a friendship, the fact that each of B and C is friends withA (provided they are mutually aware of this) gives them a basis for trusting each other thatan arbitrary pair of unconnected people might lack. A third reason is based on the incentive A may have to bring B and C together: if A isfriends with B and C, then it becomes a source of latent stress in these relationships if Band C are not friends with each other. This premise is based in theories dating back to earlywork in social psychology ; it also has empirical reflections that show up in natural buttroubling ways in public-health data.


They arestrictly optional, in that nothing later in the book builds on them. Also, while these sectionsare technically more involved, they are written to be completely self-contained, except wherespecific pieces of mathematical background are needed; this necessary background is spelledout at the beginnings of the sections where it is required. In this section, we will try formulating more concrete mathematical definitions for some ofthe basic concepts from earlier in the chapter. The discussion in this chapter has articulateda way of thinking about networks in terms of their tightly-knit regions and the weaker tiesthat link them together. We have formulated precise definitions for some of the underlyingconcepts, such as the clustering coefficient and the definition of a local bridge. In the process,however, we have refrained from trying to precisely delineate what we mean by a “tightly-knitregion,” and how to formally characterize such regions.

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Homophily provides us with a first, fundamental illustration of how a network’s sur-rounding contexts can drive the formation of its links. Consider the basic contrast betweena friendship that forms because two people are introduced through a common friend anda friendship that forms because two people attend the same school or work for the samecompany. In the first case, a new link is added for reasons that are intrinsic to the networkitself; we need not look beyond the network to understand where the link came from. Inthe second case, the new link arises for an equally natural reason, but one that makes senseonly when we look at the contextual factors beyond the network — at some of the socialenvironments (in this case schools and companies) to which the nodes belong. Often, when we look at a network, such contexts capture some of the dominant fea-tures of its overall structure. Figure 4/1, for example, depicts the social network within aparticular town’s middle school and high school (encompassing grades 7-12) ; in thisimage, produced by the study’s author James Moody, students of different races are drawnas differently-colored circles. Two dominant divisions within the network are apparent. Onedivision is based on race (from left to right in the figure); the other, based on age and schoolattendance, separates students in the middle school from those in the high school (from topto bottom in the figure). There are many other structural details in this network, but theeffects of these two contexts stand out when the network is viewed at a global level. Of course, there are strong interactions between intrinsic and contextual effects on theformation of any single link; they are both operating concurrently in the same network.

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According to the theory of strong and weak ties, with the strong triadic closure as- sumption, how would you expect the edge connecting b and c to be labeled? Give a brief (1-3 sentence) explanation for your answer.

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Based on the antibodies present in blood tests, the NSW Chief Health Officer has recently said that up to a half million Australians could already have been infected, most of them asymptomatic. On that basis, while our case fatality rate is close to two per cent, our infection fatality rate, would be more like one in a thousand, or zero point one per cent.

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With the wisdom of hindsight, not enough attention was given to keeping the virus out of nursing homes and how to respond once cases were present. Whole societies were locked down, essentially to protect the elderly, yet the elderly were still very vulnerable once the infection was among them.

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The sooner citizens don’t have to offer police an explanation for their movements, the less anxious we will feel. The sooner the airwaves are not filled by officials telling us not to go out, not to see people, and not to shake anyone’s hand, the more resilient we will be, even if there may be some modest uptick in corona cases.


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In real life, node 9 went with the instructor’s club, even though the graph partitioninganalysis here would predict that he would join the president’s club. Zachary’s original analysis of the karate club employed a different approach that alsoused the network structure. He first supplemented the network with numerical estimates oftie strength for the edges, based on his empirical study of the relationships within the karateclub. He then identified a set of edges of minimum total strength whose removal would placenode 1 and node 34 (the rival leaders) in different connected components, and he predictedthis as the split. The approach Zachary used, deleting edges of minimum total strength soas to separate two specified nodes, is known as the problem of finding a minimum cut in agraph, and it has the been the subject of extensive research and applications [8, 164, 253]. Onthe karate-club network, this minimum-cut approach produced the same split as the Girvan-Newman method: it agreed with the split that actually occurred except for the outcomeof node 9, an alignment of predictions that emphasizes how different approaches to graphpartitioning can produce corresponding results. It is also interesting to note that Zacharytraced the anomalous nature of node 9 to a fact that the network structure could not capture:at the time of the actual split, the person corresponding to node 9 was three weeks awayfrom completing a four-year quest to obtain a black belt, which he could only do with theinstructor (node 1).

One is the diameter, which we define to be the maximum distance between any pair of nodes in the graph. Another is the average distance, which — as the term suggests — is the average distance over all pairs of nodes in the graph. In many graphs, these two quantities are close to each other in value.


A recent poll showed that only 7 per cent of Australians thought that COVID restrictions were “too tough”, while 33 per cent thought them “too lenient”. Only 11 per cent thought that “getting the economy moving” was more important than “stopping the virus’ spread”, hence most governments’ tendency to make rules rather than let people make their own judgments.

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As with the Spanish Flu state border closures, only worse, it’s been every jurisdiction for itself, in a form of “pandemic protectionism”. One Australian state with virtually no corona cases won’t admit people from another state with virtually no corona cases. States that want to admit foreign students, because they need the money, don’t want to admit Australians from another state.

CLOSURE, STRUCTURAL HOLES, AND SOCIAL CAPITAL 65E C A B D FFigure 3/11: The contrast between densely-knit groups and boundary-spanning links is re-flected in the different positions of nodes A and B in the underyling social network. There is a lot of further insight to be gained by asking about the roles that different nodesplay in this structure as well. In social networks, access to edges that span different groups isnot equally distributed across all nodes: some nodes are positioned at the interface betweenmultiple groups, with access to boundary-spanning edges, while others are positioned in themiddle of a single group. What is the effect of this heterogeneity?

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In fact, the idea of using betweenness to identify important edges draws on a long historyin sociology, where most attribute its first explicit articulation to Linton Freeman [73, 168,169]. Its use by sociologists has traditionally focused more on nodes than on edges, wherethe definition the same: the betweenness of a node is the total amount of flow that it carries,when a unit of flow between each pair of nodes is divided up evenly over shortest paths.

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The latter kind of interaction —especially when we look at users directing multiple messages to others — corresponds to astronger kind of direct interaction. In a style analogous to the work of Marlow et al, Huberman, Romero, and Wu analyzedthe relative abundance of these two kinds of links on Twitter . Specifically, for eachuser they considered the number of users whose messages she followed (her “followees”), andthen defined her strong ties to consist of the users to whom she had directed at least twomessages over the course of an observation period. Figure 3/10 shows how the number ofstrong ties varies as a function of the number of followees. As we saw for Facebook, evenfor users who maintain very large numbers of weak ties on-line, the number of strong tiesremains relatively modest, in this case stabilizing at a value below 50 even for users withover 1000 followees. There is another useful way to think about the contrast between the ease of forminglinks and the relative scarcity of strong ties in environments like Facebook and Twitter. Bydefinition, each strong tie requires the continuous investment of time and effort to maintain,and so even people who devote a lot of their energy to building strong ties will eventuallyreach a limit — imposed simply by the hours available in a day — on the number of tiesthat they can maintain in this way. The formation of weak ties is governed by much milderconstraints — they need to be established at their outset but not necessarily maintainedcontinuously — and so it is easier for someone to accumulate them in large numbers. Wewill encounter this distinction again in Chapter 13, when we consider how social networksdiffer at a structural level from information networks such as the World Wide Web.

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Let’s start by positing that information about good jobs issomething that is relatively scarce; hearing about a promising job opportunity from someonesuggests that they have access to a source of useful information that you don’t. Now considerthis observation in the context of the simple social network drawn in Figure 3/3.


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Second,we observe that local bridges are precisely the edges that have an embeddedness of zero —since they were defined as those edges whose endpoints have no neighbors in common. In the example shown in Figure 3/11, what stands out about A is the way in which allof his edges have significant embeddedness. A long line of research in sociology has arguedthat if two individuals are connected by an embedded edge, then this makes it easier forthem to trust one another, and to have confidence in the integrity of the transactions (social,economic, or otherwise) that take place between them [117, 118, 193, 194, 395]. Indeed, thepresence of mutual friends puts the interactions between two people “on display” in a socialsense, even when they are carried out in private; in the event of misbehavior by one of thetwo parties to the interaction, there is the potential for social sanctions and reputationalconsequences from their mutual friends. As Granovetter writes, “My mortification at cheat-ing a friend of long standing may be substantial even when undiscovered. It may increasewhen a friend becomes aware of it. But it may become even more unbearable when ourmutual friends uncover the deceit and tell one another” . No similar kind of deterring threat exists for edges with zero embeddedness, since thereis no one who knows both people involved in the interaction.