Visualizing the Structure of Venture Capital Co-Investments

It is Friday, so I am inclined to take the liberty of posting something outside my usual tag-line areas of interest (see tag-line above). While I was out in San Francisco I met a lot of people interested in applying network analysis to their business areas or data sets. One group was TechCrunch, who had a data set of venture capital firms investments over the past two years. They had performed a some network analysis on it in the past, but were interested in getting my perspective on the data (those circular views can be so uninformative), so they handed it over to me and asked me to have at it. The image in the upper-right and the large circular hierarchical visualization below are the results of this analysis.

These visualizations combine several analytical techniques into a single view. The complexity of these images can be daunting at first; therefore, I highly recommend two things: first, allow me to walk you through how to interpret them before you begin to explore; and second, when you are ready I highly recommend viewing the above image in full-screen mode. Let’s begin!

Description of analysis

The type of network data used in this analysis is what is referred to as bipartite, or two-mode. This means that there are two distinct types of nodes in the data, and nodes of the same type cannot connect to one another. In our case, we have types as VC firms investing in start-ups, where the investment constitutes an edge between a VC and a start-up. To understand the structure of co-investments among VC firms the first step is to convert this two-mode network into a one-mode network; wherein VC firms are directly connected if they have invested in the same start-up. This network will actually help inform us as to how various firms cluster in terms of their investments, and possibly how that strategy manifests as a networked structure.

The conversion requires simple matrix algebra (multiply the two-mode matrix of connections by its transpose), which generates a square matrix of co-investment connections—with the additional benefit being that each non-zero element of the matrix represents the number of times these firms co-invested. This co-investment now represents a relative strength of tie between VC firms. The next step is to try to make sense of the massively complex network that results from this conversion. Specifically, after converting from a two-mode network to a one-mode the VC network contained 2,075 nodes with 9,443 edges—far too large and densely connected to be meaningful. To reduce the complexity of the network I performed a procedure called dichotomization, which will remove any edges that have a value below a certain threshold. In this case, I created a histogram of the edge weights and found that the most logical threshold was 3, and thus any edge between two firms that had co-invested in a start-up less than 4 times was removed. This produced the desired result, leaving me with a main component network of 205 VC firms sharing 390 edges.

Given that the motivation of these firms is presumably to invest in successful start-ups I was curious to see what—if any—natural community structures emerged from the data. Using a hierarchical community detection algorithm, I created a four-level grouping of firms based on their network structure. At each level of the hierarchy firms are more closely related by their co-investments. Next, I wanted to establish a centrality score for each firm based on their structural position as well as the relative strengths of their co-investment ties. To do so I used a centrality metric that took both of these things into account. The next, and final, step is to visually display all this information.

I have been eager to find a good reason to use a circular hierarchical visualization of a network data. There are many examples of this technique around the web web; however, I often find them less than informative. In this case, however, I think the visualization tells a compelling story.

Summary of visualization and interpretation

• Each concentric colored ring represents one of the four hierarchical clusters, with increasing granularity as you move toward the center; therefore, communities of firms become smaller at each progressive ring.
• Firm proximity in the circle corresponds to the similarity of their structure, which in this case is co-investment. That is, firms listed next to one-another are the most similar even if they are in different hierarchical clusters.
• All 205 firms are labeled, and their label size corresponds to their centrality score (denoted as HUB_SCORE in the legend at the lower-right).
• Tie between firms are sized by their weight, i.e., the number of times those firms co-invested

How I interpret this…

There are some really interesting community structures forming here. Most interesting is the community grouped in purple (1 o’clock), which includes DAG Ventures and Benchmark Capital. That community has several strong ties to the three other notable communities; grey (4 o’clock), which includes First Round Capital and Acel Partners; magenta (5 o’clock), which includes Spark Capital and Union Square Ventures; and mustard yellow (9 o’clock), which includes Kleiner Perkins Caufield & Byers. These four communities constitute the core of this network, and within that the purple group is most central. This is also clearly visible in the network visualization in the top-right of this post.

Given this emergent community structure the next step is to begin the consider all of the consequences of this structure:

• What market strategies among firms in the same community is causing these distinct network pattern?
• Why are are there not connections between firms in the grey and mustard yellow group, yet it appears everyone has co-invested with someone in the purple group? What makes these firms so influential?
• Looking ahead, can we say something about the firms in these influential communities that do not yet have a high authority score? Which among them could emerge as the next most successful VC firm?

Unfortunately, these are not questions I am qualified to answer, but I am very curious if anyone reading this has a more informed opinion. I welcome your thoughts in the comments.

Photo: Circular hierarchical network visualization generated using NetworkWorkbench

Automatically Generated Related posts:

1. Emergent Structure within the Event Sponsorship Networks of British Parliament
2. Microsoft Seadragon Great for Visualizing Large Networks
3. Visualizing Data with R and ggplot2 (video w/ slides)
4. Terrible Covert Network Structure?
5. Mimicking the Operational Structure of Terrorists to Defeat Them