I am analyzing a graph of protein-protein interactions. The data has been sourced from the STRING website.
The original directed multigraph has been converted as follows: select largest strongly connected component subgraph, then convert to an undirected graph.
Number of nodes: 3756 Number of edges: 56584 Average degree: 30.1299
During further analysis I observe that:
The graph appears to exhibit the properties of a small-world graph, namely the graph's average shortest path is small (
3.12) and its clustering coefficient is relatively high (
0.46). This, I believe, is also referred to as the
Preferential Attachment Model.
The graph's degree distribution exhibits small world properties i.e. most nodes have small degree and some nodes have very high degree.
Now, I am not a great expert in graph theory and mathematics, but I am curious to find out if the above findings are in any way contradictory, indicating a problem with the underlying graph, or whether this is indeed something that can be observed in real-world networks.