Balance in signed networks

Abstract

We consider signed networks in which connections or edges can be either positive (friendship, trust, alliance) or negative (dislike, distrust, conflict). Early literature in graph theory theorized that such networks should display "structural balance," meaning that certain configurations of positive and negative edges are favored and others are disfavored. Here we propose two measures of balance in signed networks based on the established notions of weak and strong balance, and compare their performance on a range of tasks with each other and with previously proposed measures. In particular, we ask whether real-world signed networks are significantly balanced by these measures compared to an appropriate null model, finding that indeed they are, by all the measures studied. We also test our ability to predict unknown signs in otherwise known networks by maximizing balance. In a series of cross-validation tests we find that our measures are able to predict signs substantially better than chance.

Synaptic polarity and sign-balance prediction using gene expression data in the Caenorhabditis elegans chemical synapse neuronal connectome network

“…In this work we predicted that the signbalance in the C. elegans ligand-gated ionotropic chemical synapse network is approximately 4:1 (excitatory-inhibitory, E:I). This is consistent with previous in vitro and in vivo studies of nervous systems [33][34][35][36], and also with observations of different social networks [37,38], as shown in Table 2. However, this ratio can only be predicted if not only the neurotransmitter expression of the presynaptic neuron but also the receptor gene expression of the postsynaptic neuron is taken into consideration.…”

“…The balance of excitation and inhibition-crucial for network stability-is reached via a number of mechanisms. Both synaptic and extrasynaptic, electrical and chemical, voltage-gated and ligand-gated, ion channel-mediated and G-protein coupled neurotransmission have diverse but intertwining roles in promoting and Rat excitatory neocortical neurons 20% [36] Cerebral cortex (in vivo; GAD expression) 10-20% [17] Cerebral cortex (in vivo; GABA neurons) 20-25% [17] Optimal network for synchronized bursting activity (in silico) 10-20% [6] Primary visual cortex (V1; in silico) 25% [49] Neuronal network (ex vivo) and neuronal network model (in silico) 20% [18] Wikipedia (social network) 21% [37] Epinions (social network) 15% [37] Slashdot (social network) 23% [37] University freshman network (social) 12-14% [38] https://doi.org/10.1371/journal.pcbi.1007974.t002…”

Mean-field solution of structural balance dynamics in nonzero temperature

“…Here, we build on the work of [21] and focus on the particular effect of temperature on the dynamics of balance theory. Several other studies have investigated balance theory following the same approach [25][26][27][28], although there are some differences as well. Belaza et al have written a Hamiltonian with three-body, two-body, and one-body interactions to study balance theory in political networks [25].…”

Topological Analysis of Interaction Patterns in Cancer-Specific Gene Regulatory Network: Persistent Homology Approach

“…According to structural balance theory, dyadic links holding positive and negative interactions yields four different types of triads, triangles of interactions, in the network [52][53][54][55][56] . Balance and imbalanced states of triangles are consequently determined based on the sign of the product of the links; balanced when positive (J i j J jk J ki > 0), and imbalanced or frustrated otherwise (J i j J jk J ki < 0), and their corresponding energy of a triangle, being defined as E i jk = J i j J jk J ki , constructs an "Energy landscape" for the network.…”