Degree Centrality
Degree Centrality (Freeman Node Connectivity Measure) · Also known as: node degree, degree score, DC, connectivity centrality
Degree centrality is the simplest and most intuitive measure of a node's importance in a network, defined as the number of direct ties a node has to other nodes. Normalized by dividing by the maximum possible ties, it allows comparison across networks of different sizes and is the starting point of almost every network analysis.
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When to use it
Use degree centrality when you need a fast, interpretable summary of which nodes have the most direct connections — for identifying hubs, key actors, or highly active nodes in any binary or weighted network. It suits small and large networks alike and requires only an edge list. Do not rely on degree centrality alone when the research question concerns indirect influence, information-flow efficiency, or gatekeeping roles; for those purposes, eigenvector centrality, closeness centrality, or betweenness centrality are more appropriate. It is also uninformative in complete or near-complete graphs where almost all nodes share the same degree.
Strengths & limitations
- Computationally trivial — O(n) per node — and scales to very large networks.
- Immediately interpretable: raw connection count requires no network-analysis expertise to explain.
- Applicable to directed, undirected, binary, and weighted (as weighted degree) graphs.
- Serves as an indispensable baseline for comparing more complex centrality measures.
- Degree distribution provides a fingerprint of overall network topology (scale-free, random, etc.).
- Easily visualized: node size proportional to degree conveys structure at a glance.
- Counts only direct neighbors; ignores position in the global network structure.
- A node with high degree may be entirely peripheral if all its neighbors are isolated from each other.
- Uninformative in dense or complete graphs where degree variance is near zero.
- Does not distinguish whether connections are to influential or peripheral nodes (use eigenvector centrality for that).
- Sensitive to network boundary decisions — who is included in the network affects scores.
Frequently asked
What is the difference between degree centrality and eigenvector centrality?
Degree centrality counts the number of direct connections regardless of who those neighbors are. Eigenvector centrality weights each connection by the importance of the neighbor, so a node connected to a few highly central nodes can score higher than a node with many peripheral neighbors.
Should I use in-degree or out-degree in a directed network?
The choice depends on the research question. In-degree measures how many actors point to a node (e.g., popularity, prestige, citation count). Out-degree measures how many actors a node points to (e.g., activity level, information sending). Reporting both is often informative.
Does degree centrality work on weighted networks?
The standard formulation uses binary edges. For weighted networks, the analogous measure is weighted degree centrality (also called node strength), which sums edge weights rather than counting edges. Most implementations in igraph, NetworkX, and Gephi support this option.
How large must my network be?
Degree centrality has no minimum size requirement. It is meaningful even in networks of 10 nodes. However, in very small networks the normalized score loses resolution — almost all nodes may appear equally central. For networks with fewer than about 20 nodes, examining the raw degree distribution is usually more informative than the normalized score.
When is degree centrality not enough?
When your research question concerns broker roles, gatekeeping, or information flow across the network rather than local popularity. A node with modest degree can control access between clusters (high betweenness) or reach every other node quickly (high closeness) without having many direct ties.
Sources
- Freeman, L. C. (1978). Centrality in social networks: Conceptual clarification. Social Networks, 1(3), 215–239. DOI: 10.1016/0378-8733(78)90021-7 ↗
- Wasserman, S. & Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge University Press. ISBN: 978-0-521-38707-1
How to cite this page
ScholarGate. (2026, June 3). Degree Centrality (Freeman Node Connectivity Measure). ScholarGate. https://scholargate.app/en/network-analysis/degree-centrality
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Betweenness CentralityNetwork analysis↔ compare
- Closeness CentralityNetwork analysis↔ compare
- Eigenvector CentralityNetwork analysis↔ compare
- Modularity AnalysisNetwork analysis↔ compare
- Social Network AnalysisNetwork analysis↔ compare
- Weighted Degree CentralityNetwork analysis↔ compare