Michele Coscia – Connecting Humanities

Multilayer Network Backboning

Today I want to tell a story about how sometimes science leads you to unexpected places. The main character of this story is the paper “Multilayer Network Backboning” (MNB to its friends), which I will present later this year at the CIKM conference. This was joint work with the excellent Valerio Siniscalco.

Network scientists know network backboning as the problem of identifying which edges in a weighted network are statistically significant, i.e. which ones we’re sure they actually exist. Network scientists also know other things — they’re a smart bunch — for instance that multilayer networks are networks where edges have different types. In this paper, these two worlds collide.

MNB, as a paper, didn’t really know what it wanted to do once it grew up. It was the child of another paper I wrote a while ago, about gender discrimination in the inclusion of women in Wikipedia biographies. Like all loving children, it looked at its parent with reverence, and thought it was going to go in the same line of business. See, the original paper’s entire argument relied on using network backboning to estimate the significance of edges: women had edges with greater significance than men, which suggested they were treated differently. When Valerio first proposed to write MNB, he pointed out that this was only done on the English language version of Wikipedia. Valerio wanted to see if the result also held when looking at multiple language versions.

The path for MNB, then, was clear: build the networks for a few other language versions (French, German, Italian, Spanish), redo the backboning analysis, and voila. “Voila” it was not, because as soon as you make a multilayer network you have to start asking yourself pesky questions. For instance: are we really really sure that person A linking to person B in the English edition bears no influence whatsoever on the likelihood of this A-B link existing in, say, the French edition? The entire multilayer network analysis business rests on the assumption that layers do influence each other one way or another, so we have to take such cross-pollination factors into account when estimating the likelihood of an edge truly existing. In short, we need a multilayer version of backboning.

“This is easy,” I told Valerio. “We just have to use one of the already-existing multilayer backboning methods. I’ll type in ‘Multilayer network backboning‘ on Google Scholar, pick the first random result that strikes my fancy* among the dozens available, and MNB can grow up and emulate its parent.” I did just that, and got zero hits. “Oh.”

See, maybe a normal person’s second thought after “Oh.” might be “Damn”. Not for a scientist. A scientist instead starts thanking the Gods of Science for their generous gift, and maybe does a little dance. “We know now what MNB will be. It’ll be the first backboning method that takes multilayer networks as input!” I said. “But the discrimination on Wikip…” Valerio tried to say. “The first backboning method that takes multilayer networks as input,” I kept repeating, in ecstasy, staring in the distance.

MNB, from that point onward, wrote itself. The starting point was the paper I published a while ago on single layer backboning, which established a null model based on how the two nodes linked by the edge we are testing connect in the rest of the network. One can apply it to multilayer networks as is, because one can represent them as multigraphs. But doing so results in an algorithm that considers layers independent and indistinguishable: you lose the information of which edge belongs to which layer.

MNB expands the original algorithm in two ways. First, we create a distinct null model per layer, which allows us to distinguish each layer. Then, we create an expectation estimate for each node pair to be connected which takes all layer information into account, allowing us to make the null models dependent on each other. This is based on the correlations between edge appearances in different layers, and our strategy is flexible enough to work also in the presence of anticorrelations. These happen when being connected in a layer makes the connection in another layer less likely — for instance if we have friendship and enmity layers.

The quality of the recovered backbone (y axis, higher is better) when making the test network progressively more noisy (left) or letting its layers have different levels of correlation with each other (right). The new proposed method is in green.

We can demonstrate that this works by creating synthetic networks where we control exactly which edges are signal and which are noise. The multilayer version of the backboning algorithm consistently outperforms single layer versions in recovering signal edges regardless of how much noise there is, how correlated the layers are, and other factors — as you can see from the figure above.

And the Wikipedia question? That turns out to have an interesting answer as well. In a world without MNB, we would apply the single layer backboning independently to each layer, as well as to a super-network pulling information from all languages. Doing so, funnily enough, results in a confusing puzzle: each language in isolation does not show any bias (and if anything, it is biased against men) while the aggregated version clearly shows an anti-woman bias. How could it be that the aggregated version shows the opposite of what its layers support?

The proportion (y axis) of male (blue) and female (red) profiles surviving a given backboning threshold (x axis), for the aggregated network (All) and each of its layers analyzed independently. The top row is the new multilayer method; the bottom row is a single layer version. Note how the lines flip between All and the other plots in the bottom row: from red on top to red on bottom. This does not happen in the top row.

By applying the multilayer version of the backboning, MNB in the end shows a consistent picture, where the bias is absent both in the aggregate and in each of the layers. As a result, the contradiction we got from single layer backboning disappears, although it is obviously not the final answer to the bias question — here we focus on the method, leaving in the background a number of choices that were instead the main focus of the previous paper.

So while the jury is still out about Wikipedia biases, one thing is for certain: extracting multilayer backbones is useful; it solves problems that would be difficult to handle with single layer backboning. In the end, MNB’s story has a happy ending: the paper has found its place in the world. If you want to play with the new multilayer backboning algorithm, you can find its implementation here. I’m looking forward to seeing its legacy: dozens of better multilayer network backboning algorithms in the future.

* Kids, don’t try this at home.

Comparing the Italian and Danish Music Industries

One of the blessings of being a digital humanist is being able to study something as inherently interesting as music. A while ago, I had fun trying to figure out which band was the most important in the Italian music scene. That was cool, but it left open a question, which I want to address today: are the patterns that I’m seeing specific to Italian music, or do they hold in another country?

To answer this question I needed to collect data about at least another country. Lisandro Marco Benetti and Daniel Fejerskov-Quist helped me compile a new dataset about Danish music. The result was the paper we co-authored: “Comparing the Italian and Danish Music Industries With Network Analysis,” which appeared in the journal Complexity earlier this month.

We applied the same methodology as in my previous paper to the bands releasing records in Denmark, to create a network that was directly comparable with the Italian one: bands connected to each other if they share a significant number of artists. Then, we could compare the two to figure out what stayed the same, what was different, and more.

Nodes are bands, connected by artist sharing. Node color is the average year of the band’s releases. Node size is centrality. Edge color is significance. Denmark on the left, Italy on the right.

The overall structure remained largely the same, with clear clustering by music genre and a temporal gradient, as you can see from the picture above. Sure, Denmark is smaller, has fewer bands, and a shorter time span, but overall the important structural properties of the networks are the same.

One new analysis we introduced in this paper is label nestedness. Record labels release music, so it is interesting to understand how specialized they are. When we sort labels by how much music they release, we see a nested pattern: small labels tend to focus on popular genres that are published by almost every label, while the many small specific genres are only published by the largest labels.

The dispersion of bands in the network (y axis) over time. The color background compares the observed value with what we’d expect given the number of records published. Green shows more dispersion than expected, red is less dispersion than expected (white matches expectation). Denmark on the left, Italy on the right.

Things start getting interesting when we look at the differences. For instance, by using network variance, we can quantify how much a year was innovative, by looking at how dispersed across the network the bands releasing records that year are (meaning the releases come from unrelated bands). We can control the amount of music produced, so that we know we’re not just looking at a lot of music, but specifically at a diverse body of music. The figure above shows that Denmark had its peak diversification during the 1980s and 1990s, while Italy was innovative earlier, in the 1970-1980 period.

Other differences include how the two music industries relate to different genres. Some genres show a low degree of specialization — meaning many unrelated bands have played them — in either Italy or Denmark, but not both. For instance, a diverse set of bands had tried to make beat music in Italy at its heyday, but not in Denmark. On the other hand, pop rock crops up across many unrelated Danish bands, not systematically, but this is not true in Italy. Various metal genres are also quite central in Denmark, but marginal in Italy.

The merged Danish-Italian music industry network. Nodes are still bands connected by artist sharing, with their size proportional to their centrality. Blue nodes for Italy, red nodes for Denmark.

The cool thing about this exercise is that, by using a consistent convention in making the dataset, the two networks can be merged. Artists who contributed to both Italian and Danish bands can create links across the countries. The global structure is what you see in the above figure. This significantly changes the centrality calculation. Rather than looking at the most important bands within a country, we are now looking at those bands that tie together two different countries.

Here are three examples:

Temperance: this Italian melodic power metal band is central because their records are produced by Jacob Hansen, a key figure in Danish rock / heavy metal;
Robertino: an Italian singer who was noticed at age 10 by Danish TV producer Volmer Sørensen, who launched his career;
Alex Puddu: an Italian funk artist born in Rome, but who relocated in Copenhagen at age 20*.

This has been fun, but, if you know me, you know that I don’t know when it’s time to quit. Of course the next step is to crank this up to eleven. Are the commonalities we see between Denmark and Italy just a coincidence? What if we add a third country? What if we add thirty? You’ll have to stay tuned, as I’m working on a paper to conclude this trilogy.

* To make the figure above, we used the country of origin to decide the node’s color. Alex Puddu was the one case we couldn’t quite figure out. So Lisandro and Daniel resolved to do the only logical thing, and just wrote Alex himself. He was very kind in answering, with details that would likely be appreciated by my friend Max Schich, as in the end even Alex couldn’t call himself either Italian or Danish. In the end, I flipped a coin 🙂

Criminal Activities and Migration

When something unpleasant is happening around you, the most natural reaction you might have is to try and get away from it. For instance, if you live in Mexico and there is a lot of criminal activity in the neighborhood, you might want to move, if you can afford to. This seems intuitive, but is it true? Science is often the process of systematically testing whether our intuitions about the world are true; you never know when the easy answer is wrong if you never investigate it!

This is what I did with Roxana Gutiérrez-Romero: I went back to my old love – the investigation of Mexican drug trafficking – and this resulted in the paper “Displacement and disconnection: the impact of violence on migration networks and highway traffic in Mexico” which was recently published in the Spatial Economic Analysis journal.

The question is simple: do we see a disproportionate increase in emigration (whether local within Mexico or international) from municipalities that experience spikes of criminal violence? Answering this question is quite hard, and it involves controlling for many other potential explanations that might drive emigration. Roxana did a remarkable job in figuring out how to control for those other factors, leaving me to worry about a simpler, networky question. Let’s focus on local internal migration for now.

Nodes are municipalities, connected by migration links. I’ll get to the color meaning in the text later.

We can take a snapshot of internal migration by creating a network of municipalities. Two municipalities are connected by a directed edge weighted by the number of people who change their residence from one to the other. The picture above depicts just that.

A single network doesn’t tell us much, we need two different points in time. For each pair of municipalities, we have data about the migration links for several five-year intervals (2005-2010, 2010-2015, 2015-2020). We cannot simply compare the edge weights in two subsequent snapshots, as the change we observe might be just a random fluctuation. Moreover, how do we know whether a change is significant when there are many migration links? Immigration from a municipality might have increased at the same time as all other incoming links have decreased. For this reason, the question morphs into a network science one: if we have an edge observed across two different five-year intervals with two different weights, how do we know the edge weight changed in a statistically significant way?

We got help from an unexpected ally: network backboning. Normally, network backboning is the process of determining whether an edge measured with a noisy process exists. However, by using the Noise-Corrected approach I developed with Frank Neffke a while ago, we can do more than that.

See, noise-corrected backboning achieves the task of verifying an edge’s existence by modeling it, estimating its expected weight and variance. The same edge at different times will have different weights and different variances. By using bootstrapping, a fancy word that means “draw many random numbers from a distribution characterized by the edge’s weight and standard deviation,” we can create an edge weight distribution and figure out whether the edge’s weight truly increased, decreased, or stayed the same.

This is what you see in the picture above: green edges showed an increase in migration, red edges a decrease, and yellow ones stayed about the same. We can aggregate a municipality’s net migration change, which we use for the node’s color. As a robustness check, we create the same network, but using highway traffic instead of migration:

We can use this estimation of increased/decreased migration/traffic as the variable we want to predict in a big and complicated regression that takes into account many possible alternative explanations – ask Roxana for the painfully precise details, she worked literal years on it.

What Roxana found was that our intuition is accurate: violence indeed is associated with increased emigration. We also checked international emigration to the US (which accounts for 90% of Mexican emigration) and found a similar effect: violence is associated with a 5% rise in emigration to the US and a 3% drop in return migration from the US.

So, for once, we don’t have a puzzling counter-intuitive result: we indeed see violence and criminal activity discouraging people to stay around. It would be interesting to see whether this holds in different contexts and scenarios.

A Better Way to Evaluate Money Laundering Detection Algorithms

Each day some trillion dollars change hands in any sort of financial transaction. Hidden in this money ocean there are also fraudulent actors, which attempt to sanitize illicit money by making its provenance appear normal. No one can manually verify all transactions, so there are a number of machine learning algorithms trying to spot the fraudulent ones. The problem is how we evaluate which algorithm is better than the other.

Ada Matilde Gige found an interesting problem in the normal evaluation workflow of money laundering detectors during her master work, supervised by Lasse Alsbirk and myself. This resulted in the paper I’m writing about today: “Evaluating fraud detection algorithms in a decentralized scenario“, which appeared a couple of days ago on the Royal Society Open Science journal.

The problem lies in the information the algorithms receive during their training phase. One issue with working in this field is that data is hard to come by: because it involves financial transaction, real world data is tightly controlled by the financial institutions. The solution is to use synthetic data. Luckily, IBM has created a nice, handy, and quite big dataset that simulates a world’s economy – many different banks, currencies, countries – that is free to use. In it, they injected fraudulent transactions following money laundering patterns and identified them. Naturally, it became the cornerstone of the evaluation workflow of the anti-money laundering detectors.

I’m going to oversimplify the machine learning pipeline, but essentially it works by splitting data in two parts: the training set and the test set. You can give the algorithm, say, 80% randomly selected transactions to train on. The algorithm will hopefully learn the pattern by seeing which transactions were actually fraudulent and which one were not. To know whether it actually learned, you will then give it the 20% transactions it never saw before, hide whether they were fraudulent or not, and ask the algorithm to guess.

And the algorithms guess quite well! In one version of the IBM dataset, the state of the art has a precision of 85% – meaning 85% of all flagged transactions are actually fraudulent – and a recall of 74% – meaning it captures 74% of all fraudulent transactions: a transaction has only one chance out of four to pass unnoticed.

However, Ada and Lasse argued that this standard machine learning pipeline does not work for the money laundering case. The IBM dataset contains data from different banks and different countries. If you take a random 80% sample of all transactions to train on, you’re de facto assuming that there exists an international agency that can access data from all the banks in all the countries in the world. Does this agency exist? No. Should it exist? Probably not, as it would wield an amount of power over the world that even the purest of the angels would be tempted to abuse.

What happens in the real world is that the banks will only analyze the transactions that they process directly. They will flag some transactions as suspicious and send them to the national authority. The national authority will receive only the suspicious data from all the banks. Since this is still more than can be managed manually, they will also run some sort of machine learning, to identify the most suspicious transactions. It is a two-step pipeline with some non-trivial interactions between two machine learning algorithms. This is the realistic pipeline the money laundering detectors should be evaluated with.

What happens if we do? In the same scenario as before, the precision takes a bit of a hit: it goes down from the original 85% to 75%. This is unfortunate, but not extremely critical. The real problem is with recall, which plummets from 74% to 24%. Now a fraudulent transaction has three chances out of four to pass unnoticed, the failure case has tripled!

And here’s another serving of food for thought. Remember that in this realistic pipeline we have to apply two detectors: one for the banks and one for the central authority. If we were to apply the state of the art method, the one that performs the best in the one-step evaluation, we would get a worse result, with recall going down to 7%. To get to 24% we need either the banks or the central authority to use a simpler method.

Why is this happening? Likely, it’s a combination of two things. At the first step, each bank can only use its own data. This means that each independent training set is much smaller and therefore an over-complex state of the art method might not be able to learn enough with this little amount of data. At the second step, the central authority does not receive a random sample of transactions any more, but a selected sample of the most suspicious ones. This likely breaks the assumptions on which a money laundering detector is founded.

The good news is that all of this is fixable, although it requires a lot of coordination between all the stakeholders. Banks can partner and use federated learning, each keeping their own data but being able to exploit what has been learned by the algorithm on the other banks’ data. Central authorities should coordinate with the banks and agree on which algorithms each should be using, because if these actors don’t talk and each use the state of the art method, this will likely result in a worse outcome. Finally, machine learning practitioners should use our updated evaluation pipeline in two steps to get a proper picture of how a machine learning algorithm is used in the real world.

Is What Politicians Do Similar to What they Say?

Part of the Italian lore infused on me when growing up is to be disillusioned when it comes to interactions with politicians. Assuming that what a politician promises carries information about what they’re going to do is not the wisest way of living one’s life. This is a gut feeling and it could be completely wrong. It asks for verification and data: is it true that what politicians do in parliament is not similar to how they present themselves to the public?

The data to answer this question is what the excellent Christian Ivert Andersen provided, which eventually led to the publication of the paper “Disconnect between the Public Face and the Voting Behavior of Political Representatives,” which recently appeared in the journal Applied Network Science.

Christian had spotted some promising features about how elections are handled here in Denmark. Like in some other countries in the world, Denmark has a number of voting advice applications. These apps ask politicians for their position on a number of salient issues. This allows them to place the politicians somewhere into a political ideological space. The citizen can answer the same questions and figure out which politician is the closest to them — with the assumption they should vote for them, if they do not want to heed the Italian cautionary tales.

We decided to represent this data as a network: each node is a politician and each pair of politicians is connected if they agree on a significant number of issues. Altinget was kind enough to share their data with us for our work. We’ll get to the why we represent this data as a network, but for now let’s verify whether these networks make sense:

From A to D the networks corresponding to the 2011, 2015, 2019, and 2022 elections.

It seems they do! We clearly see the two blocks (red and blue) that are the ideological coalitions typical of the Danish political environment.

This data by itself is fascinating, but not enough to answer our question. It represents the “public face” of a politician: their explicitly stated position they use to campaign and attract votes. We need a data source for the actions they take once they are elected.

Luckily, Denmark publishes excruciatingly detailed reports of parliament actions in an open format. Unluckily, such an open format is a nightmare to work with, is highly fragmented, and I’m a bit concerned about Christian’s mental health after he had worked with it (get well soon, Christian!). With this data we can build a different network, this time connecting politicians according to their voting behavior similarity in parliament:

From A to D the networks corresponding to the 2011, 2015, 2019, and 2022 legislatures.

By analyzing the connections in these two networks we can create a numerical score which summarizes the ideology of a politician, depending on the politicians they’re connected to in the network — and who they are connected to and so on. I’ve been using such score as the node color in the network pictures in this post.

So: why networks? “Why not?” I would reply as a person whose obsession with networks has now reached pathological levels. But I know that’s not going to cut it. The reason we use networks is that they allow to calculate the distance between the two ideological scores we just built — one based on the politicians’ words, the other on their actions — in a more nuanced way.

Trivially, with two ideological scores, one would simply check their difference. However, the difference between ideological scores matters most for those politicians that are supposed to be ideologically close. It matters a lot if you’re shifting your position relative to the other members of your own party, more than if you do it relatively to parties that are not ideologically similar to you.

This nuanced distance estimation can be achieved by calculating the good old network distance measure I’ve been working with for the past few years. The only issue with it is that we just get a distance value and we need to contextualize it. To do so, we compare it with a null model: we calculate the same distance but we randomly shuffle the ideological scores on the networks. This way, we know what distance we should be seeing when there is no connection between the two ideological scores on the network.

In red, the number of null models (y axis) with a given words-to-actions distance (x axis). In green, the observed distance in the real data. From A to D corresponding to the 2011, 2015, 2019, and 2022 legislatures, above row for distances calculated on the networks based on campaign words, below for distances on the parliament action networks.

Above you see the distribution of expected distances in the null model in red, and the distance we observe as the green bar. Distressingly, the green bar is to the right of the expectation, and almost always significantly so. This means that the distance we observe — the actual difference between promises and actions — is larger than what we would expect in the scenario in which the two are randomly picked! To put it bluntly: how politicians present themselves during a campaign is significantly different from what they do in parliament once elected. Looks like my Italian guts were right.

But we shouldn’t put it bluntly, not yet at least. This study is just the first step and it does require substantial robustness checks. The most important of which is that the topics representatives in parliament vote on are not necessarily the same issues they’re asked about during the campaign. The most blatant case for this is that no one had asked anything about COVID during the 2019 campaign, but we all know what politicians had to deal with starting from early 2020. We should match the votes with specific questions and use only votes sufficiently similar to at least one question to build the parliament networks. We can do this, using some natural language processing magic, so that will come next.

From these very preliminary results, the most cautious lesson learned should be: maybe be wary of making your voting decisions based on a voting advice app. There are a number or reasons — not necessarily shady, as the COVID case exemplifies — that make them not exactly a faithful representation of what you’re voting for.

Quantifying Affective Polarization on Social Media

A couple of years ago, I worked with Marilena Hohmann and Karel Devriendt on a method to estimate ideological polarization on social media: the tendency of people to have more extreme opinions and to avoid contact with people holding a different opinion. Studying ideological polarization is interesting, but it misses a crucial piece of the puzzle: what happens when differing opinions – which may or may not be trying to avoid each other – collide? Are people actually having a debate and an exchange of ideas, or are they escalating to name-calling and generally toxic behavior?

Answering that question requires a method to estimate affective polarization, rather than merely ideological polarization. Once Marilena and I were done working with the latter, we rolled up our sleeves to work on the former. The result is the paper “Estimating affective polarization on a social network“, which appeared a few days ago on PLoS One.

The objective appears simple: to try and quantify what people with differing opinions do when they interact. Unpacking this objective requires some care, though. One could think that this is a simple correlation test: if the more people disagree the more they use toxic language, then affective polarization is high.

Such an approach, however, ignores that people might hate each other so much that they refuse to communicate altogether, or they are forcibly separated. An example is r/the_donald. For a time, it was one of the most active subreddits on Reddit, creating a strong polarized environment. At some point, the Reddit admins decided to ban the subreddit altogether, which resulted in an exodus of users. In the data, one would see a decrease in affective polarization, because there was less toxicity. In reality, discourse had become so toxic it had to stop, which we argue is a sign of a growing, nor decreasing, affective polarization.

The two components of affective polarization: above, the higher the correlation between disagreement and toxicity, the higher affective polarization. Below, the more separated the camps are, the higher affective polarization is.

So we still need to track the network of interactions, just like we did for ideological polarization, because ideology and affect are intertwined. Marilena and I spent a lot of blood and tears trying to be smart about finding a solution, but in the end – as is often the case – the simple route was the best one. We decided to add the affective component to the ideological polarization measure we already had. The older measure captures the social separation, while the correlation between disagreement and toxicity captures the affective component.

Once we had such a measure, we made a case study, analyzing the evolution of the social discourse on former Twitter (RIP) on COVID-19. We used data from February to July 2020, filtered using a set of keywords used in the early pandemic debate. Initially, the results were a bit confusing. While we did find a modest rise in the affective polarization levels, it seemed that affective polarization was mostly a flat line.

The overall level of affective polarization (y axis) over time (x axis).

This went a bit counter our expectation, but analyzing the social separation and the affective components separately told an insightful story (thanks reviewer #1 for prodding us in this direction, we owe you big time 🙂 ).

Above: the affective component. Below: the social segregation component.

The clear pattern was that, in the first couple of weeks, there was low social segregation but a high affective component. After this initial shock, social segregation skyrocketed and by week 9 it plateaued, while the affective component went down.

This is consistent with a narrative of a new topic coming to scene. As the topic is new, no one knows where they stand exactly, so everyone tends to interact with everyone (low social segregation). However, feelings run high, both because of the emergency itself and – possibly – because of previous conflicts between the users, which lead to renewed toxicity. As people get used to the new scenario and the clear factions emerge and stabilize, social segregation suddenly kicks in, and the factions stop talking, which also reduces the chances of using toxic language against the opposing side.

I think this exemplifies beautifully why the measure is useful. If we didn’t have a network measure, we would conclude that affective polarization was low after the first few weeks of the pandemic, because there was no correlation between disagreement and toxicity. Instead, affective polarization was still growing, and we failed to see the correlation because polarization was so high people weren’t event talking to each other any more.

There’s more work to do, of course, because we only tested a tiny scenario. Marlena and I are working on the final piece of our polarization trilogy, where all these great tools we built are finally put to use. Stay tuned!

Finding a Connection between Kinship and Material Culture using Network Science

The past fascinates us. I often fantasize about how our ancestors lived: what did they do? How did they relate to one another? Were their social networks similar to ours? Archaeology is the way we try to answer these questions if we do not have written records. The main problem is that archaeology finds stuff — material culture. Social relationships can’t be dug up from the mud.

Together with Camilla Mazzucato and a team of archeologists and biologists, we decided to investigate whether we could actually infer the social relationships from the material culture we found. The result was the paper “‘A Network of Mutualities of Being’: Socio-material Archaeological Networks and Biological Ties at Çatalhöyük“, which appeared in January in the Journal of Archaeological Method and Theory.

The paper focuses on the site of Çatalhöyük which was inhabited in the Neolithic for several millennia. Çatalhöyük is the ideal place to draw connections between found material culture and interpersonal relationships because of some peculiar habits in the culture which inhabited the site. Upon the construction of a new building in the settlement, in fact, the habit was to bury the dead in the foundations (humans are weird).

Having lots of dead bodies is fantastic (all of a sudden I sound like Hannibal Lecter) because now in the buildings we can find material culture and human remains, both of which had a connection with the building itself. From the human remains we can infer kinship relationships between buildings, because people related to each other are buried in them.

This is where the team of biologists come in. They analyze the DNA of the human remains to establish which pairs of individuals have a first, second, or third degree relationship. Once we have both material culture and kinship relationships between buildings we can start asking ourselves whether the two correlate or not.

One way to do it is by using network variance. We can connect buildings — the nodes in the network — if they share significant amounts of material culture. Then, for a given kinship group — a set of people with at least second or third degree relationships –, we can create a numeric node attribute: how many individuals from that family were buried in each building.

The Material Culture Network of Çatalhöyük: nodes are buildings, connected if they share significant amounts of material culture. The node size tells you about the number of artifacts found in the building. The edge size is the number of common artifacts and the color is the significance level. The node color tells you how many individuals from a specific kinship group are buried in the building.

The network variance of this attribute tells us how dispersed the family is in the material culture landscape. By comparing this with a null family — a family that buries individuals at random — we can know whether the real family tended to be more concentrated in the material culture space than expected, a sign that material culture and kinship correlate. Which is what we observe!

The number of null models (y axis) with a given null family network variance value (x axis). The green band is the network variance value of the observed kinship group. Lower value = less variance = more concentrated.

There are a number of possible alternative explanations, of course. One we checked for is geotemporal proximity. Buildings nearby each other and built around the same time also share more material culture and related individuals. So we control for geotemporal proximity and we see that the effect is still significant. In other words: it is more likely for related individuals to be buried in buildings with similar material culture, regardless of when and where these buildings were built. We also check the robustness of our results by slightly changing the way we build our networks, and the way we analyze the DNA remains — the result is still there.

Our result suggests a nice consequence: it is justified to say that sites containing the same material culture hosted individuals that were related to each other. Found material culture can tell us something interesting and meaningful about the shape and dynamics of past social networks.

The Atlas for the Aspiring Network Scientist v2

After a year of dedicated effort, I’m glad to announce that the second version of my atlas for network science is finally out! Just like version one, the PDF is available free of charge both on arXiV and on the companion website, which also contains all the solutions to the exercises. If you’re a fan of physical books, you can buy it on Amazon.

Four years ago I published version one with the ambition of having a single text covering all I knew about network science in a coherent manner. The result was nice, but it had large margins of improvement. With this second edition, I aimed at improving the most egregious blind spots of the book.

The first one was about learning on graphs. Version one only had a small, confusing, imprecise chapter on this vast topic. That one chapter has blown up to four chapters, which now tackle shallow and deep learning more in depth. Of course none of those chapters get to the depth or sophistication of, say, Hamilton’s book, but I believe the value in having them in the Atlas is to show how much graph neural networks actually fit neatly into everything else from network science. They are not an extraneous body with esoteric methods: all GNNs do is adding some machine learning flavor to analyses we’ve been doing for decades, like using random walks to learn structural properties of the network.

Then, I decided to greatly expand on the background knowledge necessary to approach network science. This includes all the non-network techniques that will help you making sense of data. Again, what before was one background chapter became a whole book part with four chapters, covering probability theory, statistics, machine learning, and linear algebra.

The last major content addition is a chapter to deal with uncertain network data: what do you do when you’re unsure about the presence/absence of specific nodes/edges? There are more minor additions to the book, which are mentioned in the introduction.

Finally, last time no one yelled at me nearly enough for how tongue-in-cheek my introduction was. I took this as an encouragement to write an even more outlandish one. Fingers crossed someone will start a flame war on the social media du jour, and maybe the book goes viral and I get to retire with the $0.49 I make in profit per copy sold 🤞

Also bad news for those who want to stay healthy. All that added content means version two of the Atlas is even more back-breaking than version one:

The dinosaur is courtesy of my son.

For this book I had the additional help of a few more reviewers: Giovanni Puccetti, Matteo Magnani, Maria Astefanoaei, Daniele Cassese, and Paul Scherer. You’re very welcome to contact me if you find some more mistakes or if you have any grievances with the content — version one did ruffle some feathers.

So, if you want to become an expert on network science, a reminder: grab the free PDF on arXiV or on the website. And, if you really want to fuel my tiramisù addiction, you can always buy a physical copy on Amazon (or some other online seller). You could also go the Patreon route. I’ll see what I can cook in the next four years. Ta-ta.

My Teammates

Over the course of the last few months, I had the pleasure to find new teammates for several research projects I am involved in. I wanted to take a moment to thank them for being part of my research life — and they have the kindness of calling me their supervisor or principal investigator. Here they are, in the order they joined ITU:

Lasse Alsbirk is a co-financed PhD student and at the center of a multi-partnered research project. He will work at the intersection of the Danish Police (financial crimes section), the AI Pioneer Center, and NERDS @ ITU. His project will focus on the application and development of network science tools to fight financial crimes. He has valuable abroad experience, having received his master degree in Israel.

Anders Aagaard Kristensen joins NERDS as PhD student, coming from the University of South Denmark, where he was working on machine learning methods. His PhD project will be about the use of deep learning and generative models to understand leaves of absence in work data. The idea is to predict, simulate and, ultimately, make interventions, so that workers will have less taxing working schedules, leading to fewer leaves for sickness reasons. Anders works jointly with the National Research Center for Work Environment (NFA), which finances his fellowship and provides the data.

Nikos Salamanos joins as postdoctoral researcher, coming from the Cyprus University of Technology, where he was working on applying network analysis to study social media information dissemination. Nikos will work on an interdisciplinary Villum Synergy project on archaeological data, where he’ll develop network analysis methods to deal with highly biased and incomplete data. The idea is to test how network analysis can aid archaeological research, ultimately applying the newly developed techniques to data retrieved from the remnants of the Roman Empire. The Villum Synergy project is a collaboration with a team of archaeologists led by Tom Brughmans at Aarhus University.

Italian Music through the Lens of Complex Networks

Last year I was talking with a non-Italian, trying to convey to them how nearly the entirety of contemporary Italian music rests on the shoulders of Gianni Maroccolo — and the parts that don’t, should. In an attempt to find a way out of that conversation, they casually asked “wouldn’t it be cool to map out who collaborated with whom, to see whether it is true that Maroccolo is the Italian music Messiah?” That was very successful of them, because they triggered my network scientist brain: I stopped talking, and started thinking about a paper on mapping Italian music as a network and analyzing it.

One year later, the paper is published: “Node attribute analysis for cultural data analytics: a case study on Italian XX–XXI century music,” which appeared earlier this month on the journal Applied Network Science.

I spent the best part of last year crawling the Wikipedia and Discogs pages of almost 2,500 Italian bands. I recorded, for each album they released, the lineup of the song players and producers. The result was a bipartite network, connecting artists to the bands they contributed to. I tried to have a broad temporal span, starting from the 1902 of Enrico Caruso — who can be considered the first Italian musician of note (hehe) releasing actual records — until a few of the 2024 records that were coming out as I was building the network — so the last couple of years’ coverage is spotty at best.

Then I could make two projections of this network. In the first, I connected bands together if they shared a statistically significant number of players over the years. I used my noise corrected backboning here, to account for potential missing data and spurious links.

This is a fascinating structure. It is dominated by temporal proximity, as one would expect — it’s difficult to share players if the bands existed a century apart. This makes a neat left-to-right gradient timeline on the network, which can be exploited to find eras in Italian music production by using my node attribute distance measure:

The temporal dimension: nodes are bands, connected by significant sharing of artists. The node color is the average year of a released record from the band.

You can check the paper for the eras I found. By using network variance you can also figure out which years were the most dynamic, in terms of how structurally different the bands releasing music in those years were:

Network variance (y axis) over the years (x axis). High values in green show times of high dynamism, low values in red show times of structural concentration.

Here we discover that the most dynamic years in Italian music history were from the last half of the 1960s until the first half of the 1980s.

There is another force shaping this network: genre. The big three — pop, rock, electronic — create clear genre areas, with the smaller hip hop living at the intersection of them:

Just like with time, you can use the genre node attributes distances to find a genre clusters, through the lens of how they’re used in Italian music.

What about Maroccolo? To investigate his position, we need to look at the second projection of the artist-band bipartite network: the one where we connect artists because they play in the same bands. Unfortunately, it turns out that Maroccolo is not in the top ten most central nodes in this network. I checked the degree, closeness, and betweenness centralities. The only artist who was present in all three top ten rankings was Paolo Fresu, to whom I will hand over the crown of King of Italian Music.