Abstract
Most real networks are too large or they are not available for real time analysis. Therefore, in practice, decisions are made based on partial information about the ground truth network. It is of great interest to have metrics to determine if an inferred network (the partial information network) is similar to the ground truth. In this paper we develop a test for similarity between the inferred and the true network. Our research utilizes a network visualization tool, which systematically discovers a network, producing a sequence of snapshots of the network. We introduce and test our metric on the consecutive snapshots of a network, and against the ground truth.To test the scalability of our metric we use a random matrix theory approach while discovering Erdös-Rényi graphs. This scaling analysis allows us to make predictions about the performance of the discovery process.
Highlights
The successful discovery of a network/graph is of great interest to the Network Sciences community
We introduced in Crawford et al (2016), the two sample nonparametric test on Sequential Adjacency and Laplacian Matrix Eigenvalue Distribution
We build in the validation of our comparison methodology by using a network discovery process that produces a sequence of consecutive temporal snapshots
Summary
The successful discovery of a network/graph is of great interest to the Network Sciences community. We measure similarity of temporal snapshots of a network, as it is discovered through monitor placement, by comparing consecutive temporal snapshot (subgraphs) produced in the inference of the network. One perspective on network discovery is to consider any subgraph as one of many possible outcomes from some discovery process. For a simple graph G(V , E), with |V (G)| = n, and |E(G)| = m, there are 2m possible subgraphs on n vertices. Any discovered subgraph is one of many possible random outcomes. We build in the validation of our comparison methodology by using a network discovery process (or lighting up a network) that produces a sequence of consecutive temporal snapshots. An assumption we make is that consecutive snapshots of the network are similar, which was validated using http://faculty.nps.edu/rgera/projects.html (Gera 2015)
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