Hi Simone

This is an interesting question. I don’t have a commonly adopted strategy for you, but I do have a thought that might inspire some other ideas for you. You might want to think about what you mean by ‘closely approximate’. You appear to be setting a very strong threshold of the correct node providing the influence at the correct time. In that case, your measures seem reasonable. However, you may find that all of your different mechanisms have measured similarity values that are fairly low and not very different from each other.

In such a situation, you may want measures for the general dynamics of the diffusion rather than the specific empirical sequence. For (1), instead of measuring the order that nodes are activated, you could count the number of newly activated nodes over time and calculate distributional measures for each (mean, variance, Gini…) and/or the distance between the distributions (Kolmogorov-Smirnov…). For (2), you could measure the distribution of the number of nodes influenced by each node (so node 1 might activate 3 nodes and node 2 might activate 0 nodes etc) and again compare distributions.

Cheers, Jen

**From:** Simone Gabbriellini [mailto:[log in to unmask]] **Sent:** Thursday, 28 May 2015 10:04 AM**Subject:** how to measure the similarity between two diffusion networks

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Dear List,

I have an empirical diffusion network, where a node represent an actor and a link between actor A to actor B represent the fact that actor A influenced actor B. I have recorded, for each actor, the time he adopted the innovation.

I am trying to simulate, with different mechanisms, a bunch of diffusion networks that closely approximate the empirical one.

I have many statistics in place already, including GOF measures like degree distribution, ESP distribution and Path length distribution (a la statnet)

All these measures tell me something about the topological proximity between simulated networks and the empirical one. However, I'd like to say something about:

1/ the activation timing of the nodes

2/ if the sequence of activations (who influences whom) realistically mimics the empirical one.

Is there a commonly adopted strategy in this case?

About the activation timing of nodes, I was thinking about some sort of ranking measure. About the second point, I have no clue so far... A simple QAP correlation between empirical and simulated networks would be sufficient?

Any help more than appreciated.

Best regards,

Simone

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