# Goodness-of-Fit Tests for Inhomogeneous Random Graphs

Soham DanBhaswar B. Bhattacharya

Hypothesis testing of random networks is an emerging area of modern research, especially in the high-dimensional regime, where the number of samples is smaller or comparable to the size of the graph. In this paper we consider the goodness-of-fit testing problem for large inhomogeneous random (IER) graphs, where given a (known) reference symmetric matrix $Q \in [0, 1]^{n \times n}$ and $m$ independent samples from an IER graph given by an unknown symmetric matrix $P \in [0, 1]^{n \times n}$, the goal is to test the hypothesis $P=Q$ versus $||P-Q|| \geq \varepsilon$, where $||\cdot||$ is some specified norm on symmetric matrices... (read more)

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