Visualizing Link Communities

When YY Ahn, Jim Bagrow, and I published our paper on communities of links in complex networks, we did share the code for the algorithm, but one of the essentials missing from our package was a good way to visualize the highly overlapping link communities.

Link-communities Visualization

Thus, I’m delighted to report that Rob Spencer over at Scaled Innovation has done a great job of visualizing the detected link communities (including a new client-side implementation, I might add). The technical details are interesting and available.

The example displayed above is lifted from Scaled Innovation and shows the network of characters in The Wizard of Oz. In addition to the central visualization reproduced above (see below for details),  the page also shows the full link dendrogram and many other treats; everything is beautifully crafted. Note the community assignment matrix on the right, which is a neat way of probing the issue of nested communities. On the page, Rob has a number of interesting observations regarding visualization of the link communities and explains the layout above in further detail. I quote:

The good news is that the ABL method is powerful and flexible. The challenge is that the communities it reveals are of links, not nodes, and therefore not as obvious to portray and interpret. So far the literature method is to use a traditional force-based network diagram and color the lines between the dots, rather than color the dots. Not bad, but this has the limitations of force-directed network diagrams have always had: a big “wow factor” but of limited practical interpretive use because of the spaghetti of crossing lines. So here you’ll find outright experiments, and that means that some will be different!

In the upper circular graph the dots are the nodes and the polygons show community membership of those nodes (the colors match the table and dendrogram); line crossing is minimized by working around in cluster-joining order (same as the ROYGBIV color order). Communities are equally distributed around the circle with anchor points shown as black-centered dots; each node is placed as the weighted sum of its coordinates of each anchor to which it belongs, plus some random jitter to separate nodes with single community membership. The community ordering and coloring has an interesting result: the diagram gets simpler to see as the number of communities is increased, even far above the partition density “optimum”.

The method is fast because it’s completely deterministic and drawn in one pass, i.e. it’s not an iterative force-relaxation method.

Pervasive overlap and visualizations

While Rob’s visualization shows tremendous progress on a number of fronts (just compare it to our own – primitive – first stab at visualizing the network of characters in Les Miserables), I still think that node based visualizations of the link communities work best when we study ego-networks (a single person and her neighbors).

As we point out in the paper, we can visualize the ego-network precisely because the central node’s communities are largely non-overlapping. So in the example above, Dorothy is the Ego, placed in the center of the visualization, while the various non-overlapping story lines appear as communities surrounding her.

One of the consequences of pervasive overlap (when every node is a member of multiple communities), is that we can no longer display the communities as block structures in the network adjacency matrix. Roughly speaking, to form a block structure, we need a single block per node. Some overlap is possible within the framework of block modeling, but when we can have more communities than nodes, this approach breaks down.

A similar problem arises in visualization. My guess is that any strategy for visualizing pervasive overlap where nodes are the basis of the visualization will ultimately turn out to be problematic for a full network. One possible solution is to follow the example of CFinder and construct a visualization based on the network of communities but with the ability to zoom into each community. At the local level, Rob’s visualization would be perfect.

Comments/ideas are welcome. Note – this post can also be found at the Complexity and Social Networks Blog.

The end of Supporting Material?

Maybe this is how it happens: You see an interesting (seemingly innocuous) paper and decide to read it. Upon finding it very information-dense, you decide to take a look at the supporting information (SI) and notice that the SI has a word count greater in size than an average PhD thesis. Or maybe it’s when you decide to print the SI and realize something unusual is going on when your printer is still spitting out paper after half an hour.

However you have become aware it, scientific practice has been changing in the last few years. If I remember correctly, supporting information packages started becoming the norm for papers (at least in some journals) a only few years ago and the average SI length has been growing steadily ever since.

Now something interesting has happened. From November 1st and onwards, The Journal of Neuroscience (JNS), a leading Journal in that field, will no longer allow authors to include supplemental material when submitting new manuscripts (JNS agrees to link to non-peer reviewed supporting material on the author’s own site). The decision is explained in detail by Editor-In-Chief John Maunsell, who presents a lucid and interesting argument. He explains that on one hand, the decision was made to make the task of peer reviewing a paper more manageable, i.e. to help the referees:

Although [JNS], like most journals, currently peer reviews supplemental material, the depth of that review is questionable. Most well qualified reviewers are overburdened with requests to review manuscripts, and many feel that it is too much to ask them to also evaluate supplemental material that can be as extensive as the article itself. It is obvious to editors that most reviewers put far less effort (often no effort) into examining supplemental material. Nevertheless, we certify the supplemental material as having passed peer review.

This surely is an accurate description of the situation many referees find themselves in. Going over every equation and argument in a 100 page SI takes several days, an amount of time that most academics simply don’t have available. (In fact the current state of peer review, even without mammoth SI’s, has been argued to be suffering from serious problems.)

On the other hand the decision is also intended to protect the authors.

Another troubling problem associated with supplemental material is that it encourages excessive demands from reviewers. Increasingly, reviewers insist that authors add further analyses or experiments “in the supplemental material.” These additions are invariably subordinate or tangential, but they represent real work for authors and they delay publication. Such requests can be an unjustified burden on authors. In principle, editors can overrule these requests, but this represents additional work for the editors, who may fail to adequately referee this aspect of the review.

Reviewer demands in turn have encouraged authors to respond in a supplemental material arms race. Many authors feel that reviewers have become so demanding they cannot afford to pass up the opportunity to insert any supplemental material that might help immunize them against reviewers’ concerns.

The “supplemental material arms race” described eloquently above is another element that I, as an author, can relate to—and suspect that many others feel the same.

With no room for peer reviewed SI, each manuscript must be self contained and convincing on its own merits:

A change is needed if we are to maintain the integrity and value of peer-reviewed articles. We believe that this is best accomplished by removing the supplemental material from the peer review process and requiring that each submission be evaluated and approved as a complete, self-contained scientific report […] With this change, the review process will focus on whether each manuscript presents important and compelling results.

I think most scientists can agree that large SI’s present a challenge to the scientific method as we know it. As is argued by JNS, large SI’s present a challenge to referees and authors alike and contain the potential for a potentially harmful “SI arms race”.

But let’s consider the suggested solution. In my interpretation, the proposed solution is to introduce more trust into the process. By eliminating the peer reviewed SI, the Editor-In-Chief is effectively stating that referees should trust that the authors have done their legwork (data preprocessing, programming, statistical analysis, and other “boring” elements underlying the main results) properly.

Of course, the entire foundation of peer review is trust. As referees we begin our task trusting that authors have done their work properly and presented their results honestly. Even a good referee can only be expected to catch mistakes and problems in the material presented to him. So why not a little additional trust?

Personally, I am unsure what to think. On one side, I wholeheartedly agree that there are important problems with the current state of affairs. But, on the other side, I think that there are important arguments against allowing too much of the ‘legwork’ to left out of the peer review process. Firstly, examples of scientific misconduct are many and the elimination of peer reviewed SI will make sloppy or dishonest science easier. Secondly, and more importantly, as John Timmer at Ars Technica has recently pointed out, the increasing use of computers could potentially put an end to the entire concept of scientific reproducibility (precisely because of extensive preprocessing of data, etc). Without peer reviewed SI, this problem will even more difficult to counter.

Regardless of the pros and cons, this is an interesting move by JNS. Since JNS allows fairly long articles (typically over ten pages), getting rid of the SI might be easier for JNS and other journals aimed at specific scientific disciplines, than for highly cited interdisciplinary journals – say Science or Nature – where word-count restrictions for main text are taken very seriously.

It will be interesting to see if this policy of “no supporting material” catches on.

Pervasive Overlap

Just recently, I came across the following video showing LinkedIn chief scientist DJ Patil explaining the egocentric networks (networks consisting of an individual and their immediate friends) for a few individuals based on their LinkedIn connections.

Although the individuals in the center of these egocentric networks are unusual (in the sense that they have many more LinkedIn connections than the average user), the video clearly shows that each person is a member of multiple communities where the communities are dense and almost fully connected, while there are fewer connections between the communities. (If any of this sounds familiar, it’s because I wrote about this subject a couple of months ago on the Complexity and Social Networks Blog).

This notion of social structure implies that — seen from the perspective of a single node — everything is relatively simple: the world breaks neatly into easily recognizable parts (e.g. family,  co-workers, and friends). There are few or no links between the communities because we actively work to keep them separate (more here, on why this is the case).

I’ve been thinking about the consequences of this local structure for a while, and recently coauthored a paper this subject with YY Ahn and Jim Bagrow [1]. Here, and in an upcoming blog post, I’ll be writing about some insights from that work.

The idea I hope to explore here has to do with the global structure that arises when all nodes in a network have multiple community affiliations, when there is pervasive overlap. In the follow up, I’ll explore how a single hierarchical organization of the network can exist in the presence of pervasive overlap.

Untangling the hairball

In the standard view of communities in networks, the global structure is modular [2]. This situation is shown below (left), where the communities are labeled using different colors (image from Modular structure on the global level implies, however, that individual nodes can have only a single community affiliation!

If every node is a member of more than one community — and this is clearly the case in the LinkedIn example, as well as in real social networks — then the global structure of the network is not at all modular. Rather, the network will be a dense mess with no visually discernible structure. The network will look like ball of yarn … or a hairball (above, right). In fact, this is precisely the type of structure which has recently been discovered in empirical investigations of a comprehensive set of large networks (social and otherwise) [2, 3].

So the question becomes: How do we find network communities in the hairball? This is the question YY, Jim and I answer in Ref [1]. The trick is that although nodes have many community memberships, each link is mostly uniquely defined. For example, the link you have to one coworker is similar to the link you have to other coworkers. Thus, by formulating community detection as a question of categorizing links rather than nodes, we are able to detect communities in networks with pervasive overlap.

Using our algorithm, for example, we show that dense hairball-networks, such as the word association network (which is what is pictured above, right) contain highly organized internal structure with well defined and pervasively overlapping communities. We’re hoping that our algorithm will help reveal new insights about some of the many highly overlapping social networks, such as the LinkedIn data shown above.

Code for our algorithm may be downloaded here; that site also features a neat interactive visualization of the link clustering algorithm.

Note: This entry was originally posted on the Complexity and Social Networks Blog.