A simple network illustrating concepts used in determining embeddedness. **Node-independent paths**. There is at least one path between every node. There are also at least two node-independent paths between each of nodes 1–5. For example, between nodes 1 and 3, there are four distinct paths (1 2 3; 1 2 5 4 3; 1 5 2 3; and 1 5 4 3) but only two node-independent paths because node 2 appears in all the first three and node 5 appears in all the last three. The two node-independent paths are 1 2 3 and 1 5 4 3. As another example, there are three node-independent paths between nodes 2 and 5 (directly between them, through 1 and through 3 and 4). *k*-components. All six nodes are mutually reachable through at least one node-independent path and hence are a one-component. Nodes 1–5 are mutually reachable by two node-independent paths and since all these paths use only nodes 1–5, they are a two-component. While nodes 2 and 5 are connected by three node-independent paths, if we consider only nodes 2 and 5, only one path exists between them. The other two paths use other nodes beyond the set of 2 and 5, hence they are not a three-component. Therefore, node 6 has embeddedness of 1, and all other nodes have embeddedness of 2. Note that embeddedness captures a distinctly different aspect of sociality than does degree (the number of ties a node has). Node 6 has degree 1, nodes 1 and 3 have degree 2, and nodes 2, 4 and 5 have degree 3.

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