E-I Index
Also known as: EI index, external-internal index, Krackhardt-Stern E-I ratio, E/I ratio
The external-internal (E-I) index, introduced by Krackhardt and Stern, measures the extent to which the ties of a group point outward to other groups versus inward to its own members. It is the number of between-group (external) ties minus the number of within-group (internal) ties, divided by the total number of ties. Ranging from −1 (all ties internal, perfect insularity) to +1 (all ties external), it is a compact summary of homophily and group closure that can be computed for a whole network, for each group, or for each node.
Key highlights
- Single, bounded, interpretable number summarizing group openness versus closure.
- Computable at network, group, and node levels from the same definition.
- Requires only a network and a categorical attribute — minimal data demands.
- Permutation baseline gives a principled significance test for insularity.
Intuition
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How it works
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When to use it
Use the E-I index when each actor carries a categorical attribute (group, team, ethnicity, status) and you want a simple, interpretable measure of how internally versus externally oriented the network's ties are — at the level of the whole network, a group, or an individual. It is well suited to studying group cohesion, organizational silos, and homophily. Always compare the observed value to a permutation baseline, since the raw index is confounded by group sizes and density. For modeling homophily while controlling for other structural effects, prefer ERGM; the E-I index is descriptive, not inferential, and ignores tie direction and weight unless extended.
Strengths & limitations
- Single, bounded, interpretable number summarizing group openness versus closure.
- Computable at network, group, and node levels from the same definition.
- Requires only a network and a categorical attribute — minimal data demands.
- Permutation baseline gives a principled significance test for insularity.
- The raw index is confounded by group sizes and overall network density, so it is not comparable across networks without a baseline.
- Reduces a multi-group structure to a single scalar, losing detail about which group pairs interact.
- Ignores tie strength and direction unless explicitly extended.
- Descriptive only: it does not separate homophily from other mechanisms that generate within-group ties.
Common pitfalls
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Applications
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Frequently asked
What range does the E-I index take and what do the extremes mean?
It runs from −1 to +1. A value of −1 means every tie is internal to a group (complete closure or insularity); +1 means every tie crosses group boundaries (complete openness); 0 means internal and external ties are balanced. Most real groups fall negative, reflecting the general tendency toward homophily.
Why must I compare the index to a permutation baseline?
The expected proportion of internal ties depends mechanically on group sizes and network density: large groups and dense networks generate more internal ties by chance alone. Permuting the group labels while holding the network fixed gives the distribution of E-I values expected under random assignment, against which the observed value's significance and direction can be judged.
Can the E-I index be computed for a single actor?
Yes. The node-level E-I index counts an individual's external and internal ties and forms the same (E − I)/(E + I) ratio, measuring how outward- or inward-oriented that person is. Everett and Borgatti (2012) treat this as a categorical-attribute centrality identifying boundary spanners.
Sources
- 1.Krackhardt, D., & Stern, R. N. (1988). Informal networks and organizational crises: An experimental simulation. Social Psychology Quarterly, 51(2), 123–140.
- 2.Everett, M. G., & Borgatti, S. P. (2012). Categorical attribute based centrality: E-I and G-F centrality. Social Networks, 34(4), 562–569.
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Cite this page
ScholarGate. (2026, June 22). E-I Index. ScholarGate. https://scholargate.app/sociology/e-i-index