Calculator Inputs
Count nodes as intersections plus dead ends. Count links as street segments between nodes. For components, use 1 when the network is fully connected.
Example Data
These sample cases show how different layouts compare. Values are illustrative and may vary with counting rules.
| Scenario | N | L | Dead ends | Area (km2) | Beta (L/N) | Gamma* |
|---|---|---|---|---|---|---|
| Dense grid | 140 | 270 | 8 | 1.80 | 1.929 | 65.2 % |
| Mixed grid + loops | 120 | 210 | 18 | 2.20 | 1.750 | 59.3 % |
| Suburban loops | 110 | 150 | 42 | 2.50 | 1.364 | 46.3 % |
| Sparse collectors | 80 | 95 | 28 | 3.00 | 1.188 | 40.6 % |
Formulas Used
Counts follow standard graph measures used in transportation planning. Planar assumptions apply to typical at-grade street networks.
- Beta index: beta = L / N (links per node).
- Average node degree: dbar = 2L / N (how many links touch a node, on average).
- Cyclomatic number: mu = L - N + P (independent cycles), where P is connected components.
- Alpha index (planar): alpha = mu / (2N - 5). Shown as a percentage.
- Gamma index (planar): gamma = L / (3(N - 2)). Shown as a percentage.
- Intersections: I = N - dead ends.
- Dead-end ratio: Dr = dead ends / N.
- Density (optional): intersections per km2 = I / A, links per km2 = L / A, where A is area in km2.
How to Use This Calculator
- Define your study boundary (site, neighborhood, or district).
- Count nodes: intersections plus dead ends.
- Count links: street segments between nodes.
- Enter dead ends as cul-de-sacs and stubs.
- Set components to 1 if fully connected.
- Add area to get density metrics (optional).
- Press Calculate, then export CSV or PDF if needed.
Street Network Connectivity in Practical Design
Street network connectivity describes how easily people, services, and vehicles can move between origins and destinations using more than one practical route. In construction and neighborhood planning, stronger connectivity can reduce travel distances, improve wayfinding, and keep access functioning when a street is closed for utility work, staging, or maintenance. Connectivity is not simply “more roads.” It comes from a clear hierarchy of streets, frequent intersections, and short blocks that distribute movement across multiple paths instead of forcing every trip onto a single corridor.
This calculator summarizes that structure using graph-based measures. The Beta index (L/N) shows links per node and provides a quick sense of how richly the system is wired. Average node degree (2L/N) expresses how many street segments meet at a typical node and helps distinguish a grid-like pattern from a tree-like pattern. The cyclomatic number (L−N+P) estimates independent loops (where P is connected components). Loops matter because they provide alternate paths when one segment is congested or closed, improving resilience and route choice. For mostly at-grade street networks, the calculator also reports Alpha and Gamma as normalized percentages.
Dead ends are tracked because they strongly affect permeability. High dead-end ratios typically increase turning movements, lengthen walking routes, and concentrate trips at fewer outlets. If you add a study area, the calculator also reports intersection and link densities per km2. These density values provide scale context when comparing a compact urban core and a lower-density edge development. Density does not replace connectivity, but it helps explain whether “more intersections” reflects better structure or simply a bigger boundary.
Example data: Assume a boundary with N=120 nodes, L=210 links, P=1 connected component, 18 dead ends, and 2.2 km2 area. Beta = 210/120 = 1.75 and average degree = 2×210/120 = 3.50. The cyclomatic number is 210−120+1 = 91, indicating substantial loop redundancy. Under a planar assumption, Gamma = 210 / (3×(120−2)) ≈ 59.3%. Intersections equal 120 − 18 = 102, intersection density is 102/2.2 = 46.36 per km2, and link density is 210/2.2 = 95.45 per km2.
Use the outputs as a screening tool during concept development. If Beta and Gamma are low while dead ends are high, consider adding short connections between parallel streets, splitting oversized blocks, or introducing pedestrian and cycle cut-throughs where vehicles cannot connect. Keep counting rules consistent across all options, and note any grade-separated crossings before relying on planar indices in reports.
FAQs
1) What counts as a node?
Count intersections and dead ends inside your boundary. If you include midblock crossings in one option, apply the same rule to all options for a fair comparison.
2) What counts as a link?
A link is a street segment between two nodes. If an intermediate intersection is counted, split the segment; otherwise keep it as a single link.
3) When should I set components (P) above 1?
Use P above 1 when the boundary contains disconnected subnetworks, such as isolated service roads, separate gated areas, or construction phases not yet linked.
4) Why are Alpha and Gamma sometimes shown as N/A?
Alpha and Gamma assume an at-grade planar network and require more than two nodes. If grade separation is important, choose non-planar and use other indices.
5) Does a higher value always mean a better plan?
Not always. Very high connectivity can increase cut-through traffic on local streets. Balance connectivity with speed control, access management, and pedestrian comfort.
6) How do dead ends affect results?
Dead ends reduce permeability and concentrate movement at fewer outlets. Lower dead-end ratios often support better walking access and more reliable emergency routing.
7) How should I use the connectivity score?
Use the score to rank options quickly. For decisions, cite the underlying indices, your counting method, and any non-planar features noted in the results.