You are asking two different questions in your title and the text. I will answer the text question, explain why you are asking two different questions, and comment on the title question.
The human mind seems to have some sort of relational structure for how it works with ideas. This is usually study in the domain of memory via free recall. In a free recall experiment, a participant will memorize a list of items and then be asked to recall them in any order. Alternatively, there might be no list to memorize and instead the participant may be asked to name as many of some common things as they can quickly (for instance: name all the animals you know). The experimenter tracks the time delays between recall of items, and uses that to infer the "mental distance" between concepts.
It a typical experiment, you will see clustering effects with participants quickly naming a bunch of objects of one type before taking slightly longer to transition to another type and then name many objects of that type quickly. As an example, I might be asked to name cartoon characters and I would start listing:
"Bart" [short delay] "Homer" [short delay] "Marge" [short delay] "Lisa" [short delay] "Maggie" [long delay while my mind switches from 'The Simpsons' cluster to 'Futurama' cluster] "Fry" [short delay] Leela [short delay] Dr. Zoidberg [etc]
This suggests that I naturally connect and infer different relationships between ideas. In particular, the temporal structure of my recall reveals that I known concepts like "The Simpsons" and "Futurama" and I connect certain names to each other because they share a relationship of "being on the same show". Of course, how I structure my categories and recall is shaped by my expertise.
As an experimenter, I could represent the way people structure their ideas as a graph/network, with individual ideas represented as nodes and closely related ideas (or ones between which people usually transition often or quickly) connected by edges. Free recall is then a random walk on this network. The netwok is similar to a social network, except there nodes are people and edges exist between friends. However, just because what you are studying has a network structure, doesn't mean that it has "6 degrees of separation".
The "6 degrees of separation" idea is a subset of all networks that are known as small-world networks. Small-world networks are defined as networks on $n$ nodes where the longest shortest path (i.e. the fewest edges you need to follow to get from any arbitrary node to any other arbitrary node) is of length about $\log n$. Many networks, say a regular grid, are not small-world (in the case of the regular grid, the length of the longest shortest path is proportional to $\sqrt{n}$ which is much bigger than $\log n$). Thus, the question in the body of you post is not necessarily related to the title.
However, if we take a highly clustered small-world network and perform a random walk on it, then the results will be similar to what we see in free recall experiments. In particular, the random walk will tend to wander for a while in one cluster until taking a jump to another cluster where it would again linger. Thus, the relational structure of ideas might be consistent with small-world networks.
