## Lecture 4: Characterizing Network Structure

## Lecture Overview

Having completed our general introduction to the course and figuring out how to depict networks, we’re moving on to the question of structure. Structure involves patterns, and there are patterns involving ties, parts of networks and whole networks for you to learn. It is very important that, before you work on this lecture, you first read our chapter for the week: “The Basics of Network Structure.” It’s available online at http://www.umasocialmedia.com/socialnetworks/wp-content/uploads/2016/09/TheBasicsOfNetworkStructure.pdf.

## What’s “Central” in a Social Network?

This week’s readings introduce a number of ways to characterize the structural circumstances of nodes in a network or the structural characteristics of a network as a whole. To clarify differences between how different measurements of network structure are made and what they signify for the structure of a network, let’s calculate all of these for a sample network containing seven people and the undirected relations between them. (I encourage you to generate your own slightly different network and practice making your own measurements in order to further familiarize yourself with them.)

*Degree*

For the above network, perhaps the simplest measurement to make is that of degree. In an undirected network like the one you see above (a network in which the ties have no arrowheads and indicate *no direction*), the degree of a node is the number of ties connecting it to other nodes in the network. In a digraph (or “directed network,” a network in which the ties DO have arrowheads, indicating some *direction*) two different measures — *in-degree* (ties coming in to the node; loosely, *popularity*) and *out-degree* (ties coming out from the node; loosely, *gregariousness*) — would be made.

Finding degree is as simple as counting. For this network:

Degree

Ann: 3

Bert: 2

Celine: 2

Dan: 2

Ella: 2

Fred: 2

Gina: 1

While it’s true that Bert, Celine, Dan, Ella and Fred each have two ties associated with them, their positions in the network differ in ways that aren’t captured by the measurement of degree. Look again at our sample sociogram. Fred and Ella each have two ties to other people, but Ella is tied to people who are in turn tied to more people. Fred is also slightly farther away from most of the other nodes in the network than Ella. Bert and Ella are each tied to the popular Ann, but Ella is the only conduit to her other alter (Fred), while there are alternative paths to Bert’s other alter (Celine) that don’t involve Bert. In order to capture these aspects of Fred and Ella’s structural positions, we’ll need to measure aspects of their *centrality* that include information about more nodes in the network other than Fred, Ella and their immediate alters.

*Betweenness Centrality*

Betweenness centrality captures another aspect of importance in a network — the ability to act as a bridge between other nodes, the ability to connect otherwise unconnected others. These individuals can direct the flow of information across a network because they are given the power to either pass information on or not. The cooperation of a between-central node will be in demand. A node with low betweenness, on the other hand, may be redundant because there are other paths by which one might cross from one side of a network to another. A low-betweenness node may also be at the edge of a network, literally peripheral.

To review from the reading, to calculate betweenness centrality for a node of interest (let’s call it *Node* *X)*, follow three steps:

- Find and make a list all geodesic paths between all pairs of nodes in a network. When there are two or more paths that are equally short, include them all.
- In the second step, for each pair of nodes in the network, note the fraction of geodesics in which your
*Node X*is in the middle of the geodesic. - In the third step, add all these fractions up. The result is the betweenness centrality score for
*Node X*.

Here is a video that reviews betweenness centrality using an example of cities:

For another example, let’s return to our sample network for the lecture. In that network the betweenness centrality of **Bert** is 2, the result of adding up the following fractions:

+ (1/2) for the two Ann-Celine geodesics, one of which includes Dan and the other of which includes Bert,

+ (1/2) for the two Ella-Celine geodesics, one of which includes Dan and the other of which includes Bert,

+ (1/2) for the two Fred-Celine geodesics, one of which includes Dan and the other of which includes Bert,

+ (1/2) for the two Gina-Celine geodesics, one of which includes Dan and the other of which includes Bert,

+ (0/1) for the Ann-Ella geodesic,

+ (0/1) for the Ann-Fred geodesic,

+ (0/1) for the Ann-Gina geodesic,

+ (0/1) for the Ella-Fred geodesic,

+ (0/1) for the Ella-Gina geodesic,

+ (0/1) for the Fred-Gina geodesic,

+ (0/1) for the Dan-Ella geodesic,

+ (0/1) for the Dan-Fred geodesic,

+ (0/1) for the Dan-Gina geodesic.

The betweenness centrality of **Celine**, on the other hand, is only 0.5, the result of adding up the following fractions:

(1/2) for the two Dan-Bert geodesics, one of which includes Celine and the other of which includes Ann,

+ (0/1) for the Ann-Ella geodesic,

+ (0/1) for the Ann-Fred geodesic,

+ (0/1) for the Ann-Gina geodesic,

+ (0/1) for the Ella-Fred geodesic,

+ (0/1) for the Ella-Gina geodesic,

+ (0/1) for the Fred-Gina geodesic,

+ (0/1) for the Dan-Ella geodesic,

+ (0/1) for the Dan-Fred geodesic,

+ (0/1) for the Gina-Dan geodesic,

+ (0/1) for the Bert-Ann geodesic,

+ (0/1) for the Bert-Ella geodesic,

+ (0/1) for the Bert-Fred geodesic,

+ (0/1) for the Bert-Gina geodesic.

Even in a small network, finding the geodesic distances between all pairs of nodes can be tricky to accomplish by sight, because the number of pairs in a network, n*(n-1) where n=the number of nodes, grows quickly as a function of size. Fortunately, you’ll soon learn how to use the computer program *R* to calculate network measures like this automatically for networks of any size, even for networks with many thousands of nodes.

*Closeness Centrality*

Closeness centrality is important because human beings have a horizon of observability beyond which they are unaware of the activities of others. In 1983, sociologist Noah Friedkin published the results of a research project in which he studied the awareness professors had of one another’s research. Very quickly professors had no idea what their peers were doing: at a network distance of two, one biological science professor was aware of another biological science professor’s work only 9.2% of the time at the University of Chicago and only 6.5% of the time at Columbia University. Even fewer professors were aware of one another’s work when they were at a network distance of three from one another. Farness is fog. Closeness is clarity.

To make this idea concrete, the closeness centrality of a node *is equal to 1 divided by the farness of a node*; closeness is literally the inverse of farness. The farness of a node, in turn, is equal to the sum of geodesic distances between that node and all other nodes in the network.

Revisiting our sample network, Ann has a closeness centrality of 0.1 because she has a farness of 10. Ann’s farness score is the sum of her network distance to Bert (1), Celine (2), Dan (1), Ella (1), Fred (2), and Gina (3).

Gina, on the other hand, has a closeness centrality of 0.0526, the inverse of her farness score of 19. Gina’s farness score of 19 is the sum of her network distance to Fred (1), Ella (2), Ann (3), Bert (4), Dan (4) and Celine (5).

Practice calculating closeness centrality with the interactive “thinglink” image you see below:

*Density*

The concept of the density of a social network is simple. Network density is a fraction: the number of **actual ties** in a network divided by the number of **possible ties** in a network. Because the number of actual ties can never go below zero and can never exceed the number of possible ties, the result varies between 0 and 1. When multiplied by 100, it represents the percentage of all possible ties in a network that are actually in the network.

The number of actual ties in a network is simply a matter for counting, and finding the number of possible ties is only a little more complicated. If ** n refers to the number of nodes in a network**, then in a directed network, the number of possible ties is calculated as

*n*(n-1)*. In an undirected network, the number of possible ties is calculated as

*(n*(n-1))/2*.

The density of the sample undirected network in this lecture is 0.33333, because there are (7*6)/2 = 21 possible ties in between the 7 nodes, and 7/21 of them are actually present.

Of all these measurements of network structure, I’ve found students seem most mystified by the measurement of density. Why does the formula for density look the way it does? In this brief video, I try to demystify the formula for network density — particularly the part that involves the calculation of the number of possible ties:

Density, betweenness centrality, and closeness centrality are three of the trickiest measurements of network structure. That’s why we’ve devoted extra space to them here. However, I describe a number of more straightforward measurements of network structure in the textbook readings. Below is a review video that covers the concepts of *distance, degree, indegree, outdegree, directed network, undirected network, path, and cut point*. I hope you find it helpful:

## Using Centrality to Uncover an Epidemic

At this point, there may be two words hovering in your mind: “So What?” Who cares, you may ask, about all the different sorts of centrality that may appear in a network? Why would such measurements matter, except to the overly fussy?

Do you consider the subject of the deaths of thousands upon thousands of people every year to be overly fussy? If not, then you have your answer.

Tens of thousands of people in the United States alone die every year from influenza and flu-related symptoms. Across the world, between a quarter of a million and half a million people die from the flu every year. What if it were possible for physicians to detect a flu outbreak earlier? It is possible, and network analysis of centrality makes that possible.

In “Social Network Sensors for Early Detection of Contagious Outbreaks“, social network analysts Nicholas Christakis and James Fowler begin with the class size paradox discovered by Scott Feld that your friends have more friends than you do. Christakis and Fowler take that insight and stretch it, noting that your friends not only tend to have a higher degree centrality than you, but also tend to have a higher betweenness centrality than you. They then cite the research of Robert M. Christley et al 2005, who find that individuals with a higher degree centrality and a higher betweenness centrality have a greater risk of infection and are more likely to be infected early in a disease outbreak.

Christakis and Fowler take that network insight applied to disease outbreak and propose an intervention — what if doctors don’t simply ask an individual whether s/he is experiencing flu symptoms? What if doctors also ask if an individual’s *friends* have been experiencing flu symptoms? In their research regarding the real spread of H1N1 flu among Harvard undergraduate students, they find that focusing on the symptoms of higher-degree and higher-betweenness *friends* uncovers signs of flu in a community up to two weeks earlier than current methods.

This method, derived from measures of social network centrality, could buy more time for public-health measures to curb the extent of an outbreak of the flu, possibly saving lives.

## Density, Distance and Network Size

One of the interesting things about the density of a network is that it *declines* quickly as the size of a network *increases*. This is true because density equals the fraction (# actual ties)/(# possible ties) and the numerator (top value) of the fraction changes differently from the denominator (bottom value) of the fraction as the number of nodes in a network increase.

The number of actual ties in a network depends upon the typical degree centrality in a network. Here’s how. If we consider the relation of close friendship, we might imagine the typical node has about five alters, leading to a degree of 5. Some nodes will have a higher degree and some will have a lower degree, but if the average node has a degree of 5, the number of actual ties in a social network will be equal to the *number of nodes times 5*:

The denominator of the fraction describing network density, the number of possible ties, behaves differently than the numerator as the number of nodes (called *n*) increases, increasing exponentially. In a digraph, the number of possible ties = *(n*(n-1))*. In an undirected network, the number of possible ties = *(n*(n-1))/2*. Whether ties have direction or not, the number of possible ties will increase more quickly than the number of actual ties as network size increases:

Some people refer to this tendency as a *bug, *a problem for comparing the density of networks of different sizes, but it also can be thought of as an interesting *feature* of social networks. In a 1982 book and a 1981 journal article, Claude Fischer and Noah Friedkin consider the possible differences in the social networks of small towns (with small network size) and big cities (with a large network size). It is an unavoidable truth (as long as we have limited time to maintain a limited set of social relations) that the overall network density will be smaller in a big city and higher in a small town.

Does this mean that people in cities are doomed to live unconnected lives, to know people who in turn don’t know one another? Not necessarily; Claude Fischer finds that in the big cities as well as the small towns of California, the density of the networks immediately surrounding people tends to remain high. That high density in a city comes at a cost: to keep up that high density among your friends, your friends will have to stop associating with other people in the city, keeping the overall density of the city low. People in cities will know a few people very well, but most people not at all.

## Walkthrough: Building a Family Network

It’s time for you to stop simply thinking about social networks and start constructing them. This week, you have **a homework assignment due** (see the syllabus under “Week 4” for details); you should find, complete and upload the assignment by following the “Homework” link on our course Blackboard page. In that assignment, I ask you to to place a matrix and a social network graph for your family into a Microsoft Word document. Word is part of the Microsoft Office suite. Because you are a UMA student, Microsoft Office is now available for you to install on your own computer for absolutely free. To get yourself a free copy of Microsoft Office, visit this page and follow the instructions posted there.

To put a matrix in your Word document, try using the *Insert->Table *command. If your matrix won’t fit that way because it’s just too darned big, try *Insert->Table->Excel Spreadsheet*. That second option can put in a table of any size into your word processing document.

To put a social network graph in your Word document, try using the *Insert->Shapes *command. There are plenty of node shapes, lines and arrows available for you to use there.

Be sure to pay attention to a few details in your homework:

- In the matrix you create, every node is represented in one row and one column, never in two rows or two columns.
- Furthermore, even if two nodes are members of what we’d informally consider to be the same “family,” that doesn’t mean they’ll be tied in this formal network — because in this formal network, a tie
*only exists between spouses/partners or parents and children*.

These features are no accidents. It may take a bit of time to get used to, but one of the best features of social networks is that they measure exactly what they say they measure and *no more*. As you start head out on your own in future weeks to describe the world around you using social networks, you will have to be very careful and precise when deciding what you intend a social network to measure.

## What Centrality Matters? When?

This week, I won’t ask you to participate in the course lecture by posting to Padlet. Instead, I want you to gain participation credit by posting comments at the end of this lecture (using the “leave a comment” form). Your comments should address two points:

1) Is there an aspect of the readings for this week or the course lecture that you don’t understand? If so, work hard to identify exactly what definition, piece of information or example confuses you or seems wrong somehow — and ask a smart question that gets to the core of the issue. Try to avoid vague complaints “I just don’t understand this lecture” or “the reading is so hard” — mostly because there’s little I can do with them. Also avoid general requests like “could you cover betweenness centrality again?” because they don’t provide direction The questions I’m looking for show me what you know before they ask about what you don’t understand: “All right, Prof. Cook, I understand that closeness centrality for Node X involves adding up the geodesic distances from Node X to all other nodes. But why you do you then take 1 and divide it by that number? What does that step accomplish?” That’s the kind of question I’m looking for: one that helps to iron out problems but requires you to have taken a few steps forward already.

2) Look at this network: a somewhat-famous “kite” network popularized by network pioneer David Krackhardt (1988):

Which node is most central in this network? The answer depends on the kind of centrality measure you use. By degree centrality, d is the most central node. But by betweenness centrality, h is the most central node. Finally, by closeness centrality, f and g are tied for the most central node.

Node d, Node f, Node g or Node h: which node matters most in this network to you? Why? And what does your answer have to do with the meaning of degree and of different forms of centrality?

I look forward to reading your thoughts!

## References

Christakis, Nicholas A. and James H. Fowler. 2010. “Social Network Sensors for Early Detection of Contagious Outbreaks.” PLoS ONE 5(9): e12948.

Christley, Robert M., G. L. Pinchbeck, R. G. Bowers, D. Clancy, N. P. French, R. Bennett and J. Turner. 2005. “Infection in social networks: using network analysis to identify high-risk individuals.” American Journal of Epidemiology 162(10): 1024-1031.

Fischer, Claude. 1982. *To Dwell among Friends: Personal Networks in Town and City.* Chicago: University of Chicago Press.

Friedkin, Noah. 1981. “The Development of Structure in Random Networks: An Analysis of the Effects of Increasing Network Density on Five Measures of Structure.” *Social Networks* 3(1): 41-52.

Friedkin, Noah. 1983. “Horizons of Observability and Limits of Informal Control in Organizations.” *Social Forces* 62(1): 54-77.

Krackhardt, David. 1988. “Predicting with Networks: A Multiple Regression Approach to Analyzing Dyadic Data.” *Social
Networks* 10: 359-381

1.) The confusing part of this lecture to me is finding the betweenness centrality. What I am having a difficult time with is determining which ties and nodes I need to focus on to find this. When I was trying the examples, I didn’t understand why the node at the end (but is tied to two other nodes) wouldn’t be considered as being in between, or in the middle. I am also getting lost with the fractions of betweeness centrality.

2.) I felt that centrality is the most important. The person or node that is the center of the communication affects each of the other nodes. My eyes immediately gravitated to node d. I made the connection to work. I could picture the principal in the place of node d, and the teachers outreaching that node. I don’t feel that the distance from or closeness was a essential to the relationship in that sense. I didn’t see distance as necessarily a negative, rather as a positive that the networking was reaching beyond a small circle.

Hi, Tamee! Thanks for asking a question. It’s always hard to be the first! I love the google-eyed conclusion.

The answer to your question about “why the node at the end wouldn’t be considered as being in between, or in the middle,” is right there in the question. A node is “between” along a network path if it has at least one node on either side of it along the path. A node on the end is not between two other nodes. That means it’s not counted when calculating betweenness.

For getting lost in the fractions, do you mean it’s just a lot of fractions to keep track of (definitely true!) or that you are having trouble figuring out the way to complete the calculation? If it’s the latter, could you provide an example?

In your answer to part 2, could you specify ***what kind*** of centrality you feel is most important? Thanks!

1.) Thanks for clarifying. That makes more sense to me that it wouldn’t be on the end. I saw it as a connection, not as a continuum. TO clarify the fractions, I am having a hard time completing the calculations. I did watch all the videos, but perhaps I need to review them again?

2.) Sorry…I meant degree centrality because my eyes immediately gravitated to node “d”, which is the most central node.

Yes! Review is always helpful. If after review you still can’t figure out why a centrality measure ends up the way it does, call me at 207-621-3190 and we can talk about it!

My question is about the first video, “Thinking About Betweenness Centrality (UMA Social Networks).” Are there certain factors that affect the importance of betweenness centrality’s importance? The examples you used were logistical. Often, route drivers select a certain route and stick to it, for a myriad of reasons. They may know other ways, and use them as alternatives, but one path is normally chosen. Factors in logistics could be slope of land, amount of traffic, food or favorite break areas, and even personal connections living in a certain area. I realize these may or may not be similar to a social network and the affect on nodes. The point of the question is that there are other things to consider besides the location of a node, isn’t there, when determining betweenness centrality or looking at structure? Or should one merely look at the physical structure first before delving deeper?

Hi, Scorpius! Thanks for asking this interesting question. I think what you’re asking is, “are sometimes some network paths considered preferable to others?” That’s a really neat idea. Perhaps there’s something attractive about the nodes along the way, perhaps there’s something about the connections themselves, right? Yes, yes, yes, that’s definitely possible in the real world!

The calculation of betweenness centrality covered here ***does not*** take such factors into account, but you could modify the betweenness centrality measure to do so, by for instance giving more attractive paths a greater weight. Again, that’s not what this betweenness centrality measurement does, but you **could** modify the betweenness calculation to account for such considerations. If you’re really interested in the idea, check out this article, about halfway down the page: https://toreopsahl.com/tnet/weighted-networks/node-centrality/

1.) Thanks for clarifying. That makes more sense to me that it wouldn’t be on the end. I saw it as a connection, not as a continuum. TO clarify the fractions, I am having a hard time completing the calculations. I did watch all the videos, but perhaps I need to review them again?

2.) Sorry…I meant degree centrality because my eyes immediately gravitated to node “d”, which is the most central node.

I think that the hardest part of this week’s lecture would have to be keeping track of all of the numbers and using the formulas to measure each density or centrality! I like examples and doing my own to fully get it, which I think the separate videos (and examples in lecture-did well).

Another part of the lecture that was hard to grasp were the sections on closeness centrality of a node. They are equal to 1 divided by the farness (or closeness of a node). Determining the farness of a node is equal to the sum of geodesic distances, which is slightly confusing. In the example below that section, there’s a sample network where Ann has a centrality of .1 and a farnness of 10.

Ann’s farness score is sum of her network distance to Bert (1), Celine (2), Dan (1), Ella (1), Fred (2), and Gina (3). I guess I am not quite sure how to figure this out. Is it another equation such as the n(n-1)?

Hi, Betelgeuse! The formula for this is Closeness Centrality(node A) = 1/(Sum(geodesic distance of node A to all other nodes)), but that’s just another way of saying what has already been said in lecture and readings. I’m glad working through examples is helpful to you. :)

1)This week’s videos and reading helped me to better understand networks. I learned that the significance of studying networks is far reaching. It is interesting that by studying social networks scientists can look at data that could help stop or at least contain an outbreak of the flu. When I signed up for this course I didn’t really know anything about social networks but I was interested to learn about them. Though we have been given tons of information this week, I feel as though I understand most of it. I just need to take a bit of time to digest and practice the formulas and steps involved in finding centrality of a node, whether it be betweeness centrality, closeness centrality or degree. Which form of centrality is most preferred to be used to study social networks or are they all commonly used together to really see the whole picture of any given subject of study?

2) The node that matters most in your network example is either F or G. The closeness centrality they represent is very important when it comes to communication. By being the closest to other nodes overall, these nodes are able to influence the other nodes in a much more direct way. They are also privy to more information in that they are able to witness more and hear more from the network as a whole. Because of their close connections to many nodes the information is passed more quickly and accurately. There is something you said in your first lecture that has really stuck in my mind: “It is not what you are , it is who you know!” ( Or at least that is what stuck in my mind!) I agree totally. Many famous actors’ children also grow up to be famous actors, not just because the parents are, but because of the connections they have through their parents. Often job promotions are the result of not only being in the ‘right’ place at the ‘right’ time but also knowing the right people. It is all about communication and connecting!

Hi, Vega! When I started to study social networks I asked the same question: “but which centrality measure is best?” I think that I’d answer your question now, much later in my life, by saying that which centrality measure is best depends on what idea of centrality you want to capture. Popularity? Indegree centrality. Gregariousness? Outdegree centrality. Being in the middle of threads of gossip? Betweenness centrality. Easier access to lots of others in the network? Closeness centrality. It’s because “centrality” can mean so many different things that we have different measures of centrality.

1.) Overall, I found the readings and lecture this week to be very informative. The videos in the lecture helped me to better understand the process of network structure. I consider myself to be a “visual learner” which is why I appreciate the videos that have been posted in the lectures thus far. Our weekly reading, “The Basics of Network Structure” was also helpful to comprehend the different formulas involved with network structure. The reading was also useful in terms of definitions– when I stumbled upon a word I was not familiar with, the list of definitions helped me to piece everything together by knowing what “foreign” words mean. In my opinion, the lecture and reading this week were very clear. I am starting to become very interested in the study of social networks. I also found the lecture video containing flu statistics very interesting.

2.) The node in the diagram above that is the most significant has to be “d.” In terms of degree centrality, d is considered to be the most central node, meaning it will have some of the strongest ties. I believe that d is the most important because it plays a large role into how the other nodes interact– most of the other nodes have to go through d to communicate. D is definitely a node of power.

Sagitta, glad to hear that you’re doing well. This class is pretty well aligned for visual learners with the network graphs and all. Please do let me know if you run into troubles!

1. The hardest part of the homework this week was creating a proper network graph. I know it is difficult to address that in the comments. Could I schedule a time to discuss what I did right or wrong when creating my network graph? I feel as though I spent too much time on that part of the assignment and want to make sure I understand it better before moving on. Thanks!

2. In the graph I found D to be the most central node because I used degree centrality when looking at it. D appears to have the most and strongest ties therefore making it the most important node.

Christopher,

I hear you, and the answer is absolutely yes! Would you like to send me an e-mail to james.m.cook@maine.edu and let me know the times that would be best for you?

1. I found this weeks lesson has been a lot of information but I believe I have a decent grab on it all. I am still trying to get a better grasp on finding centrality of a node. I was wondering if there was a preference of which form of centrality is used depending on what the subject matter is? Is it a personal preference? Is it dependent upon the outcome that is being researched?

Overall, I found watching the videos to be e tremendous help. I never thought of myself as being a visual learner but I would definitely have to say that I would probably be lost in this class if it wasn’t for your videos. Another thing that I have found to be very helpful is printing out the different terms every week and keeping a copy on my desk to refer back to.

2. I believe that the node (D) is the most significant node as it is the central node with the most ties to it.

Hi, Phoenix. See comments above, but in short, yes! which centrality you choose to use depends on what kind of centrality you want to research. In the second part of your question, for instance, you are prioritizing popularity, and that’s degree centrality.

Okay…so I’ve re-watched the first video on Betweeness Centrality a few times and I still have questions regarding the “wrinkles” when we add a road from Beaverton to Flooville. I was able to see the following relationships and had the following questions:

ABC ABF ABCD ABFE ABCE (they equal 1 because same geodesics)

CBF CEF (equals 1/2 for Beaverton and Flooville?

DCBF DCEF (equals 1/2 but why for Beaverton and Edgerton? Why doesn’t it count toward the centrality for Charville?

BCE BFE (equals 1/2 for Charville and Flooville?

DCE DCB DCBA DCEF DCBF( 2/2 for Charville)

So in summary, at 12:30 in the video I don’t understand why Beaverton and Edgerton gets the 1/2 for path DCBF and not Charville.

Hi, Auriga! DCBF does indeed count 1/2 toward the betweenness centrality score for Charville. DCEF also counts 1/2 toward the betweenness centrality score for Charville. Together, 2 out of 2 (2/2) geodesics from D to F involve Charville (C). This is discussed in minute 13 of the video. Hope this helps.

1.This weeks lesson has a lot of information to grasp. After I rewatched the videos a couple times and wrote some notes down it came together. Also reading everyone’s questions and Professor James Cook’s comments really helped me get a good understanding on this week’s lesson. The videos are great information, they get to the point and are good lengths. I find that a benefit of taking online classes is that you can always re-read or re-watch something if it seams unclear to you.

2. I would consider node D the most important. It stuck out to the most to me right when I looked at the network. Which would be degree centrality meaning it is the most central node.

1) I think I am understanding it but it’s overwhelming to have so many new concepts and try to “see” them all at once in the network. I think I am going to have to review the reading and video’s again (possibly when my mind is more”available” to accept more information) and draw the samples out myself. Im having a hard time starting with one aspect and working through it and then being able to move to the next while remembering all that I did with the first. The video’s help tremendously, I just have to re-watch more times and I think I can get it. I am going to take another day on this homework because I can’t seem to put it all together still. ( I may be reaching out)

2) I feel like h is the most central as it appears that way in the networks look (based on the nodes you mentioned and not all of them) but ties with g and f with nodes in closeness proximity (3). But F,G and H all have the same distance’s between in closeness….

Libra

Libra, thanks for writing. Please DO reach out. This material does take practice, but I would also be glad to work through this material with you either in person, over the phone, or by video chat. I look forward to hearing from you!