Table 1. Summary of multi-resolution methods for network diagnostics.

Technique	Method Summary	Control Parameter	Strengths and Limitations	Refs.
Soft Threhsolding	Raise each entry in to the power r:	r: power applied to entries in . Small r limit weights all connections equally. Large r limit amplifies strong connections, relative to weak.	Enables continuous variation of the contribution of edges of different weights. Strong edges may dominate, but all connections retained.	[49], [50]
Windowed Thresholding	Construct binarized network a fixed percentage of connections corresponding to a range of edge weights	: average edge weight of connections within the window. Small isolates weak connections. Large isolates strong connections.	Enables an isolated view of structure at different edge weights. Weak connections are not obscured by strong connections, but relationships between strong and weak connections are ignored.	[15], [49]
Modularity Resolution	Structural resolution tuned in community detection. Sets a tolerance on the partition into modules relative to a null model.	: appears in the quality function or optimized when dividing nodes into partitions. Small yields one large community. Large yields many small communities.	Enables a continuous variation in the resolution of community structure. This method has the most direct, tunable control of the output, but does not generalize to diagnostics other than those associated with modularity.	[51]

We use soft thresholding, windowed thresholding, and variation in the resolution parameter of modularity maximization to probe network architecture across scales (Column 1). For each approach, we provide a method summary (Column 2), a description of the control parameter (Column 3), a brief synopsis of the strengths and limitations of the approach (Column 4), and a few relevant references (Column 5).