Collective memory, consensus, and learning explained by social cohesion

Abstract

Humans cluster in social groups where they discuss their shared past, problems, and potential solutions; they learn collectively when they repeat activities; they establish social norms; they synchronize when they sing or dance together; and they bond through social cohesion. A group is more cohesive if its members are closer together in their network and are bonded by multiple connections. Network proximity and redundancy are indicated by the second smallest eigenvalue of the Laplacian matrix of the group network, called the algebraic connectivity. This eigenvalue is key to explaining and predicting the outcomes of said activities.

Figures (6)

• Figure 1: Two networks of the same size and density were used in a mnemonic convergence experiment (adapted from Coman et al. 2016). ( a) Network with $\lambda_2 = 0.333$. ( b) Network with $\lambda_2 = 0.074$. ( c) Memory convergence in network a (continuous lines) and network b (dotted lines) according to the diffusion equation (Eq. 1).
• Figure 2: Node coloring experiment. (a) Network with six clusters and a tie-rewiring probability of $p = 0.1$ (adapted from Kearns et al. 2010). (b) Time (in seconds) to reach consensus as a function of the algebraic connectivity of the network. Note that the data (circles) was obtained for given chances of random tie relaying, but here, pertinent levels of algebraic connectivity are plotted. The predictions from the original myopic heuristic model (in seconds) are shown in triangles.
• Figure 3: Algebraic connectivity is bounded by mean distance. ( a) Random graphs with skewed degree distributions (size range $[10, 50]$; density = 0.3) and the upper bound of $\lambda_2$, based on Eq. \ref{['eq:distance2']}. ( b) Random graphs with Poisson degree distributions (same sizes and density as in a) with Eq. \ref{['eq:distance2']} fitted to the data.
• Figure 4: Network distance and connectivity. ( a) Time to task completion with mean distance in the node coloring experiment. ( b) Algebraic connectivity with mean distance for square lattice networks (length range [2, 25]). Compare with the random networks in Fig. 3 (main text). ( c) Algebraic connectivity with node-independent connections between two groups. Initially, the two groups were separate cliques (each, $n = 30$); subsequently, independent connections were placed between them while making them sparser to keep density constant (inset). ( d) For chordless cycles with a length $l \geq 6$, cross-connecting them midway (or almost midway, when the number of nodes is odd) decreases their mean distance by a magnitude shown on the vertical axis.
• Figure 5: Cycles and chords. ( a) A triad (smallest cycle) embedded in a network ($\lambda_2 = 0.382$). ( b) The triadic tie from network a is relayed to cross-connect the largest cycle in a way that reduces the mean distance ($\lambda_2 = 0.430$). ( c) The triadic tie from network a is relayed in a way that increases the mean distance ($\lambda_2 = 0.329$).