The paper “Polarization and multiscale structural balance in signed networks”, co-authored by LASIGE’s integrated researcher Andreia Sofia Teixeira, was published in the journal Nature Communications Physics (SCIMAGO Q1). The work is a collaborative effort between LASIGE, the University of Warsaw, the University of Trento, and the University of Kansas.

In the world of networks, Structural Balance Theory (SBT) has been a go-to framework for understanding how positive and negative connections, like friendships or conflicts, shape group dynamics. Born from Gestalt psychology and fine-tuned by Cartwright and Harrary, SBT has intrigued sociologists, network physicists, and computer scientists.

At its core, SBT delves into splitting a network into groups that don’t get along—a feat only possible when all cycles in the network are positive (meaning the product of the signs are positive). Yet, real-world networks rarely play by these rules, sparking the search for nuanced measures like Degree of Balance (DoB). These measures aim to measure how close a network is to being perfectly balanced by examining the balance between positive and negative cycles.

However, practical challenges muddy the waters of this seemingly straightforward task of adding up signs to understand structural balance. Counting cycles is a demanding computational challenge, especially in big networks where their numbers explode. Furthermore, figuring out how to combine DoB across different cycle lengths adds a layer of complexity, making it tricky to get a complete picture of network balance.

In the team’s last paper in Communications Physics, they present the Multiscale Semiwalk Balance (MSB) framework—a recent game-changer. Drawing inspiration from past approaches, especially the walk-based method suggested by Ernesto Estrada and Michele Benzi in 2014, MSB steps up as a practical and flexible solution.

What Sets MSB Apart:
Efficiency: MSB takes a shortcut by estimating cycles with closed walks, using straightforward linear algebra for counting.
Versatility: MSB is a universal fix, ready to tackle any (simple) signed network, be it directed and/or weighted.
Multiscale View: MSB brings a detailed and broader perspective to DoB, shining a light on the importance of shorter walks.

The MSB framework, a considerable contribution to the study of SBT, skillfully tackles the challenges, offering a clearer view of network dynamics. We evaluate real-world data, like re-examining Sampson’s Monks dataset and exploring cooperation ties in the U.S. Congress, proving MSB’s strength. It not only outperforms previous methods but also reveals the social forces shaping changing network structures.

Last but not least, the paper is accompanied by a user-friendly Python implementation of all the measures defined in our framework. With this contribution, the team hopes to offer a valuable resource for a variety of scholars interested in studying polarization, signed networks, and structural balance. They proposed a consistent and general SBT framework that is applicable to all kinds of simple signed networks (also directed and/or weighted), while also being an efficient computational tool allowing scaling of SBT-motivated analyses even to very large systems.

The paper is available here.

Legend to the above image:
Examples of high and low polarization and its general connection to frequencies of balanced and unbalanced cycles. The two networks depict bill co-sponsorship relations in the U.S. Senate. Positive ties (blue) link senators, who tended to promote the same bills together more often than by chance, and negative ties (red) correspond to those who collaborated less often than at random. The four triad diagrams depict four possible strongly (un)balanced undirected 3-cycles. Positive ties are marked with blue and negative with red dashed lines. a 96th Congress (1979–81, Carter administration) was a period of low polarization with frequent positive between-party and negative within-party links. b 114th Congress (2015–17, Obama administration) featured high polarization with in-group ties being almost exclusively positive and out-group ties negative. c Schematic depiction of the relationship between relative frequencies of (un)balanced cycles and low polarization, which is characterized by comparable frequencies, or more rarely by a majority, of unbalanced cycles (note that, even though only 3 cycles are depicted, the general relationship pertains to cycles of all lengths). d Relationship between (un)balanced cycles and high polarization, which implies that there is a clear majority of balanced cycles.