Hairball - Grab from the Heart Technique

Hairballs are harsh graph structures that are mainly hard to visualize. This is because;

It is hard to visualize over 1000 nodes and 2000 edges like shown at the above snapshot. It is named as Hairball because its congested structure. I obtained that graph from PPI network of Plasmodium_falciparum_3D7 published with the article PubmedID:16267556. Mainly, it is hard to see anything from the visualization. We can only infer that there are highly connected structures inside hairball.

What will happen when grab from the heart technique. Let's see:

We randomly select some nodes and grab from the graph. The resulting graph stays with less than 1000 nodes and edges. Then let's see what happened to level-1 grabbed part:

Here, there are less than 500 nodes and at least three times number of edges. This is also another hairball. Next let's grab another heart from the hairball and see:

The resulting graph is sparse and nodes/edges are clearly visible. Then we should check level-2 grabbed part:

It is again hairball :). Still can not understand the pattern, nodes and edges. Let's continue with level-3 heart then:

Edges/Nodes number are getting less. What about level-3 heart then:

Now it is not insane graph. Complicated but not like hairball.

What I understand from this post, hairball can be visualized in such pattern. Level-by-level visualizations from top to deepest level by grabbing from heart technique.

Visualization of Turkey City Map as Graphs - Travelling Problem For Different Cities Perspective as Tree

What will happen when we remove all unused edges from the previous post(link).

You will see tree like below. I only provide Ankara,Istanbul and Izmir snapshots;

Ankara

Istanbul

Izmir

Visualization of Turkey City Map as Graphs - Travelling Problem For Different Cities Perspective

Before we introduced our approach for Istanbul(link) only, "what will happen when case of other cities" is a good question. There are some other crowded cities in Turkey like Izmir, Ankara, Bursa, etc.

See below results for all such cities;

Ankara

Antalya

 

Bursa 

Diyarbakir 

Erzurum 

Adana

  

Izmir

Konya 

Trabzon

Hakkari 

Visualization of Turkey City Map as Graphs - Travelling Problem

In the previous article, we showed how Turkey city graph has nodes with weights. Now, we are going to present how edges can also weights. Meanwhile, we will add some colors to our city graph and use edge weights to show Turkey's traffic problem at the beginning and end of long holidays.

Let's define the problem as follows;

Turkey has a great city named Istanbul where it is located at north-west of Turkey. It is not only attractive place for Turkish citizens but also citizens of other countries. As a result, more that 14 million people live in Istanbul and it takes attention from all around cities from Artvin to Hakkari and Hatay to Sinop. So, during long Islamic Eid holidays, especially at the first and last day, imagine that people are trying to reach their home city designated from Istanbul. With this post we will show this traffic with weighted edges(let's imagine thicker lines on the map).

So let the game begins;

The first visualization above, shows how direction of traffic occurs originated from Istanbul. It does only relies on neighborhood connection between cities(currently not depend on road connections). Red lines show the traffic flow.  In essence, it is a tree when gray edges are deleted. Please observe the tree from below snapshot;

One observation is about that tree:

The hierarchy begins from Bolu where it is observed to be critical points of holiday traffic.

You should also observe that, colors are provided with the tree. Colors are given according to the distance to Istanbul. Hakkari with green color requires to pass 11 cities to reach Istanbul (It is far to Istanbul with units, 12 cities). Meanwhile, Tekirdag, Kirklareli and Izmit are also in the same color and distance to Istanbul is only 1 city. Now, let's see how colors are visible when the positions are coming from original positions on the map;

Then, let's apply some interesting layouts such as organic layout for the sake of our appetite;

So, in the end, let's get into the problem:

The flow of traffic from Istanbul to other cities. In the problem, we define travelling problem of each people that was not born in Istanbul. We assume that all these people need to travel to their home cities. The number of people travelling from Istanbul to any city is defined with the proportion of the population. We know Istanbul is the largest city and second is Ankara, then Izmir. As a result, we can say that travelling people from Istanbul to Ankara is taken proportion from Istanbul population as much as Ankara's population divided by Turkey's population. That process is defined for all other cities rather than Istanbul.

Next, the travelling path is also another problem. We have a tree above. So regarding to that when someones needs to travel from Istanbul to Ankara, needs to pass through Izmit-Sakarya-Bolu path. So, we define the path for each cities originated from Istanbul.

Finally, each path should contain traffic to next and next cities. So the traffic from Istanbul to Ankara should be carried on Izmit, Sakarya and Bolu as well.

So that is the result;

According to this result, Turkey's first highway between Edirne-Ankara is built just in right direction. But from Edirne to Istanbul part should have been built through Istanbul-Canakkale direction. Moreover, there is a new bridge construction between Izmit and Yalova. According to result, that bridge is also built on the right path. In the meantime, there should be highway from Bursa-Eskisehir-Konya in the future because Konya seems to be hub point in the center. Meanwhile in the east part of Turkey, Erzurum seems to be regional hub. And, there should be highway between Ankara-Erzincan-Erzurum path. Also, highway between Adana-Gaziantep in the south of  Turkey is in the right position.

Thanks for reading.

Flow From Istanbul to Other cities of Turkey

Nodes have weights and Red edges show the flow