Figure 16

Illustration of test and reference sets for statistical tests performed in Sects. 4.2–4.4. (a) illustrates the relationship between different sets of investor nodes. Investors who synchronize their trades with at least one social connection are a subset of investors who synchronize their trades with at least on other investor, which is a subset of investors who have their trading accounts matched which is a subset of all investors in the network, i.e., \(\mathcal{I}^{\text{CON}\text{-}\text{SYNC}} \subset \mathcal{I}^{ \text{SYNC}} \subset \mathcal{I}^{m} \subset \mathcal{I}\). (b) illustrates the links that constitute the test and reference sets used in Sect. 4.2. The main test set consists of all pairs of investors who are both socially connected and synchronize their trades (CON-SYNC). The main reference set includes pairs of socially connected investors who do not synchronize their trades, of which at least investors is known to synchronize trades (thus green color squares) with one of its’ direct connection (CON-NSYNC). The robustness reference set (\(\text{CON}\text{-}\text{NSYNC}^{*}\)) includes only those socially connected investors who have matched trading accounts (thus orange squares, \(\text{CON}\text{-}\text{NSYNC}^{*} \subseteq \text{CON}\text{-} \text{NSYNC}\)). (c) illustrates the links that constitute the test and reference sets used in Sect. 4.3. The main test set (PATH-SYNC) consists of all pairs of socially connected investors who are on the shortest paths between pairs who synchronize their trades but are not directly connected in the social network. This may include pairs that synchronize (green color) or not (blue and orange color) their trades. The reference set (NPATH-SYNC) includes pairs of investors who are not on shortest paths between directly not connected investors who synchronize their trades. The for the robustness tests we use further restricted sets (indicated with ^∗) with pairs of investors who have matched trading accounts. (d) illustrates the links that constitute the test and reference sets used in Sect. 4.4. The main test set consists of all pairs of investors who are both socially connected and synchronize their trades (CON-SYNC). The reference set (NCON-SYNC) includes pairs of investors who synchronize their trades but are not socially connected