The common neighbor bias is a measure of the tendency of neurons to form clusters that are more strongly interconnected than expected. It is similar to the clusterin coefficient, but has been generalized in the following ways: First, it takes the directionality of connectivity into account. Second, it can also characterize the connectivity between two disjunct populations of neurons. Third, it takes into account (i.e. it normalizes for) the distance-dependence of connectivity between neurons.

Formally, the measure characterizes by how much the number of neighbors in the graph of synaptic connectivity is increased for a pair of neurons when a connection exists between the pair. Traditionally, the tendency has been expressed as "the connection probability between the pair increases with the number of common neighbors", but this assertion is functionally identical to "the number of common neighbors is higher for connected pairs". The measurement is defined for a combination of source population (S), target population (T) and neighbor population (N). The neighbor population specifies which neurons are considered as potential common neighbors; from source and target population we pick the pairs of neurons to analyze, where the pair is considered to be "connected" if at least one synaptic connection exists from the neuron in the source to the neuron in the target population. Here, we used as the neighbor population the entire model, i.e. any neuron is considered a potential common neighbor. Finally, one can calculate the effect on pre- or postsynaptic common neighbors.

The bias is then calculated as follows: First, a "raw bias" is calculated as the ratio of the mean number of (pre- or postsynaptic) common neighbors for connected pairs divided by the value for unconnected pairs. To take into account the effect of distance-dependence, the value is normalized using a control model: All considered pairs are grouped into distance bins with a width of 50 um. Then, the numbers of common neighbors for pairs are shuffled within each bin. The ratio of raw bias to bias in the control model is the "normalized bias". A second approach aims to measure the effect of distance-dependence and connectedness at the same time: Based on sampled from all pairs, we fit a linear model as follows:
CN = x * C + y * D, where CN is the number of common neighbors (pre- or postsynaptic) of a pair, D the distance between them, and C is 1 for a connected pair, or 0 otherwise. The value of x is then serves as a measure of the common neighbor bias ("fit-based bias").