Beyond 150: Modeling Social Circles with Dunbar’s Number

Recently I tried to promote my new book (mentioned at the end) while also researching WeChat Moments. WeChat now allows up to 10,000 friends, but most people haven’t reached that limit; even high‑profile figures like Zhou Hongyi have very large networks, which can be troublesome.

Friends vary in closeness, which is influenced not only by personal preference but also by physiological constraints.

British anthropologist Robin Dunbar introduced the concept of the Dunbar number, the approximate limit of stable social relationships a person can maintain—about 150. Dunbar based this on the brain’s processing capacity, especially the neocortex volume related to social networking.

Dunbar Number

Dunbar compared brain sizes and group sizes across primates and found a proportional relationship between neocortex capacity and the number of stable social contacts. Applying this to humans yields an average upper bound of 150 stable relationships.

Dunbar also identified hierarchical social layers:

Intimate circle (≈5 people): closest family and best friends.

Close friends (≈15 people): important friends affecting life quality.

Friend circle (≈50 people): broader acquaintances with regular interaction.

Social circle (≈150 people): all stable contacts, the core Dunbar number.

Extended network (≈500‑1500 people): familiar faces known but interacted with infrequently.

Each layer differs in interaction frequency and emotional investment, shaping expectations and effort.

In modern organizations, the Dunbar number guides team design; many companies limit groups to no more than 150 members to ensure sufficient attention and participation.

Although social media enables connections with thousands, the Dunbar number reminds us that quality outweighs quantity, as the brain’s capacity limits stable relationships.

As a mathematical modeling enthusiast, I wondered whether we could quantify and classify people based on the sizes or proportions of these layers, then explore similarities and differences among individuals.

Social Model

The core of the model is a vector representation of a person’s social circles. Each dimension corresponds to the number of contacts in a specific layer (intimate, close friends, friend circle, social circle, extended network).

Intimate circle (≈5)

Close friends (≈15)

Friend circle (≈50)

Social circle (≈150)

Extended network (≈500)

Based on the vector, individuals can be categorized:

Socially active : high values in broader layers, indicating a wide network.

Intimacy‑dependent : high value in the intimate layer, relying on a very small close circle.

Balanced : relatively even values across layers.

Reclusive : low values in all layers, indicating a small network.

These types suggest possible career inclinations:

Socially active – suitable for public relations, marketing, sales.

Intimacy‑dependent – suitable for research, artistic creation.

Balanced – suitable for management, education.

Reclusive – suitable for programming, accounting.

Similarity between two people can be measured by the cosine similarity of their social‑circle vectors, while difference can be quantified by Euclidean distance.

For example, person A (balanced) and person B (socially active) show high cosine similarity (similar distribution) but a noticeable Euclidean distance (difference in the extended network layer).

This vector‑based approach helps understand individual social traits, career tendencies, and can be applied in HR management and social‑network analysis to design more effective interaction strategies and team structures.

Below is a brief introduction to my upcoming book Modeling: The Mathematics of Thought , which will present a DEED framework and 20 key problem‑solving mindsets with quantitative methods. Stay tuned for its release around mid‑May.