Spot the Difference!
Illustrating Network Properties
By Allison Link
In network science, there are certain properties that can be observed across many different kinds of networks. Whether they are examining social networks or biological networks, researchers use these properties to understand the interactions between nodes. Below are several pairs of network graphs. In each pair, one of the graphs shows the presence of a specific network property and the other shows the absence of that same property. Try out your network science skills by seeing if you can spot the different relationships between nodes. Then, read the blurb to learn more about each property and find out whether you guessed correctly!
These two network graphs represent differences in small-worldness. Graph 1 represents a small-world structure: most of the nodes do not have direct connections with each other, but distant nodes can be reached by “traveling” along a small number of edges. A real-world example of this can be seen in social networks, where two strangers can often be linked by one or two shared acquaintances. Graph 2 does not have small-world structure, as each node is directly connected to many other nodes within the network. Generally speaking, small-world networks are more efficient as the average “path” between nodes is shorter.
The degree of a node refers to the number of connections it has with other nodes. High-degree nodes share lots of connections, while low-degree nodes may only be connected to a few nodes. Assortativity is a feature of networks where nodes that are similar in degree tend to be connected. Graph 2 in this pair is an assortative network, since low-degree nodes are connected to other low-degree nodes (this can be seen at the edges of the network), and high-degree nodes are connected to each other (this can be seen in the middle of the network). Graph 1 is disassortative, since many low-degree nodes are connected to a single high-degree node. This is represented by the branch-like connections throughout the graph. A real-world example of a disassortative network is the interactions between job recruiters and people seeking employment. Recruiters interact with many potential applicants for a job, whereas those applicants are unlikely to be interacting with each other.
While both of these graphs have the same number of nodes, they differ in their community structure. This refers to the presence of communities, which are groups of nodes that share connections within their group but have few connections outside of it. Graph 2 has community structure, since there are several modules that are sparsely connected to each other. Graph 1 does not have a strong community structure since its nodes are well connected and lack distinct modules. We often seen this kind of structure in metabolic networks, where modules represent different pathways or cycles that occur within a biological cell.
