First, thank you all, including Oliver, bigreddmachine, iisurge, and anonymous others, for reading, responding, and discussing the posts in this thread.

Oliver Those terms are difficult to comprehend because they are the same words in our daily conversation with different, perhaps generalized or specialized, meaning or definition. For example, when we talk about “random” in math or science, we need to also specify the probability mass function (pmf) or probability density function (pdf) to convey the exact meaning, such as laudney mentioned the “geometric distribution” (if I remember correctly) in some other thread. However, in daily conversation, “random” is a quite vague concept or accompanied with a uniformly distributed pmf or pdf.

bigreddmachine Thank you for the detailed comments. I understand that the network is NOT the blockchain. A blockchain is a de-centralized, distributed data storage system.

In order to further clarify the thoughts I try to discuss, I think I should make the terms clearer:

- Blockchain: The de-centralized, distributed data storage system. This is the target I would like to understand and study.
- Node: In the case of Reddcoin, I mean a full operational wallets, storing and processing blockchain data. Browser wallets are not included.
- Network: Apparently, the term here does not mean the Internet. It means the whole thing consisting of nodes, defined in 2, connecting to each other.
- Vertex: Node. I prefer to use the term “vertex” when considering nodes in the level of mathematical abstraction such that the practical, physical notion of (computing) nodes can be removed.
- Edge: The TCP connection between nodes. They are actually directed edges. If you do a getpeerinfo command, you will see your node connecting to some other nodes (Inbound: false) and being connected by some other nodes (Inbound: true). Sometimes, there are multiple connections from one node to another. To simplify the model, as long as there is a TCP connection from A to B, we consider the directed edge A->B exists, no matter how many TCP connections.
- Graph: The thing consisting of vertices, defined in 4, and edges, defined in 5, is called a graph, which is a mathematical representation of the network, defined in 3.

After abstracting the real-world, physical situation as mathematical objects, there are different levels to study. Cryptocurrencies exist as working (complex) systems. There are many facets of them, including at least

- They are considered as currencies (or at least we hope that they can play the role). At this level, economists are actively discussing this new thing and predicting the possible outcome. As I indicated in the previous post, this facet is being addressed in academia.
- Cryptocurrencies are a (significant) application of the blockchain technology. I am interested in conducting research at this level. I would like to know, as the thread topic, the properties and characteristics of blockchains. Blockchains exist on some communication network. The current implementation is established on the TCP/IP network, and hence, we can define the edges of the “graph” by using TCP connections. If in the future, the architecture changes (e.g., NDN, named data networking), we can use some other way to define the graph. By doing so, the blockchain itself may be deeply, theoretically investigated without heavily confined by the software implementation or the physical configuration.
- The current blockchain technology is based on two major components: One is communication network (mostly the TCP/IP network for now), and the other is Cryptology. Both of them are well developed, and it is why the blockchain technology works. Needless to say there are many scholars working on the two realms in academia.

Hence, I am going to focus on the blockchain technology. As the first step, I wish to know how the graph, i.e., “network structure,” affects the functionality of the blockchain. I understand that it is impossible to fully separate this layer from the underlying mechanism, including the software implementation, and/or from the current currency application, but I will try my best.

Of course, all kinds of discussion on any facets of the related topics are welcomed. The blockchain technology is brand new in human history. I feel lucky to see it happens in my life time.