Supplemental Material: CHIP: A Hawkes Process Model for Continuous-time Networks with Scalable and Consistent Estimation

The spectral clustering algorithm for directed networks that we consider in this paper is shown in Algorithm A.1. Theorem B.1 provides an upper bound to the error rate of spectral clustering on the weighted The effect of this term is negligible as T, so we ignore it. We now present an upper bound on the error rate for communities (analogous to Theorem B.1) estimated from the unweighted adjacency matrix The upper bounds on the error rates in Theorems B.1 and B.2 are not very informative in terms of In Section 4.1, we considered a simplified special case Similarly, we have the following result for spectral clustering using the unweighted adjacency matrix A . 3 Theorem B.3. Hence the unweighted adjacency matrix has a 1 in almost all entries, and the community structure cannot be detected from this matrix. The density of the aggregate adjacency matrix is governed by the parameters of the CHIP model.