DSP: A Statistically-Principled Structural Polarization Measure

Post-hoc normalization via randomization tests remains fundamentally unprincipled, as it applies arbitrary null models retroactively without rigorous justification.

“Attempts to correct these biases, such as post-hoc normalization via randomization tests [38], remain fundamentally unprincipled, as they apply arbitrary null models retroactively without rigorous justification.”

• cites [38] [38] Ali Salloum, Ted Hsuan Yun Chen, and Mikko Kivelä. 2022. Separating Polarization from Noise: Comparison and Normalization of Structural Polarization Measures. Proceedings of the ACM on Human-Computer Interaction 6, CSCW1 (March 2022), 1-33. sourceDisputed

  Section 3 (Methods; page unavailable) specifies what each null model preserves and explains why randomization is used to separate structural bias from polarization, rather than presenting the models as arbitrary. Section 5.3 (Normalization of the scores; page unavailable) reports that every normalized score outperformed the best unnormalized score. The paper uses and supports this approach; it does not characterize it as fundamentally unprincipled. (LLM, conf=0.88)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured

Overall, denoising [38] often moves the polarization scores away from their ideal values rather than correcting them.

“Overall, denoising [38] often moves the polarization scores away from their ideal values rather than correcting them.”

• cites [38] [38] Ali Salloum, Ted Hsuan Yun Chen, and Mikko Kivelä. 2022. Separating Polarization from Noise: Comparison and Normalization of Structural Polarization Measures. Proceedings of the ACM on Human-Computer Interaction 6, CSCW1 (March 2022), 1-33. sourceDisputed

  Section 5.3 says denoising corrects for the expected effects of network size and degree distribution, and reports improved performance for all scores after normalization. The Discussion (Section 6) recommends the procedure because it removes substantial noise. The paper does not describe denoising as often moving scores away from ideal values; it reports the opposite effect on its evaluation measures. Page numbers were not available in our copy. (LLM, conf=0.90)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured

The proposed solution of standardizing the RWC score by its values in a random graph null model requires considerable computational resources.

“In addition, it requires considerable computational resources.”

• cites [38] [38] Ali Salloum, Ted Hsuan Yun Chen, and Mikko Kivelä. 2022. Separating Polarization from Noise: Comparison and Normalization of Structural Polarization Measures. Proceedings of the ACM on Human-Computer Interaction 6, CSCW1 (March 2022), 1-33. sourcePartly supported

  Section 5.3 (page unavailable) says normalization requires randomizing the network multiple times and recomputing the score; the authors sampled each network 500 times. This supports the claim that the procedure involves repeated computation, but the paper does not characterize its resource requirements as considerable. (LLM, conf=0.78)

  Experimental — accuracy not yet measured

DSP removes the biases found in the original Random Walk Controversy by eliminating the problematic role of predefined influencers.

“Our design explicitly removes the biases found in the original Random Walk Controversy (RWC) [15], by eliminating the problematic role of predefined influencers.”

• Also stated in: § Abstract · p. 1 · plain

  “DSP removes the arbitrary concept of 'influencers' used by the popular Random Walk Controversy (RWC) score, instead treating every node as a potential origin for a random walk.”

• cites [15] [15] Kiran Garimella, Gianmarco De Francisci Morales, Aristides Gionis, and Michael Mathioudakis. 2018. Quantifying Controversy on Social Media. ACMTransactions on Social Computing 1, 1 (2018), 3. - sourcePartly supported

  The Results > Synthetic data section reports a limitation of Random Walk Controversy (RWCG): it misses changes in opinion polarization because it bisects the network into two communities. Our copy does not identify predefined influencers as the source of that limitation or say that removing them eliminates bias. The citing authors’ statement about their own design is not a finding attributed to this source. (LLM, conf=0.78)

  Experimental — accuracy not yet measured

RWC has systematic bias.

“A key critique of RWC (as well as of other measures) is its systematic bias [38].”

• cites [38] [38] Ali Salloum, Ted Hsuan Yun Chen, and Mikko Kivelä. 2022. Separating Polarization from Noise: Comparison and Normalization of Structural Polarization Measures. Proceedings of the ACM on Human-Computer Interaction 6, CSCW1 (March 2022), 1-33. sourceSupported

RWC reports positive polarization scores on random Erdős-Rényi networks where edges are independent and no true structural division exists.

“The measure reports positive polarization scores on random Erdős-Rényi networks, where edges are independent, thus no true structural division exists.”

• cites [38] [38] Ali Salloum, Ted Hsuan Yun Chen, and Mikko Kivelä. 2022. Separating Polarization from Noise: Comparison and Normalization of Structural Polarization Measures. Proceedings of the ACM on Human-Computer Interaction 6, CSCW1 (March 2022), 1-33. sourceSupported

The proposed solution of standardizing the RWC score by its values in a random graph null model is post-hoc.

“Second, the solution, while widely applicable to all measures, is post-hoc.”

• cites [38] [38] Ali Salloum, Ted Hsuan Yun Chen, and Mikko Kivelä. 2022. Separating Polarization from Noise: Comparison and Normalization of Structural Polarization Measures. Proceedings of the ACM on Human-Computer Interaction 6, CSCW1 (March 2022), 1-33. sourceSupported

Assortativity alone is insufficient to explain the overall level of polarization of a network.

“Additionally, existing studies additionally indicate that assortativity alone is insufficient to explain the overall level of polarization of a network.”

• cites [33] [33] Leto Peel, Jean-Charles Delvenne, and Renaud Lambiotte. 2018. Multiscale mixing patterns in networks. Proceedings of the National Academy of Sciences 115, 16 (2018), 4057-4062. - sourceCould not verify

  The Introduction (p. 2) and section 2 (p. 7) argue for measuring polarization with network modularity rather than relying on spatial-model measures. A search for “assortativity” found no passage addressing whether assortativity alone is insufficient, so our copy does not verify the specific claim. (LLM, conf=0.75)

  Experimental — accuracy not yet measured

In a bi-colored clique with 5000 vertices, DM presents a positive bias on balanced partitions.

“DM, which also presents a positive bias on balanced partitions”

In monochromatic-splittable networks, as alpha decreases, the value of DSP tends to its maximum attainable value n/(2(n-1)).

“Thus, the value of DSP tends to its maximum attainable value 𝑛 2 ( 𝑛 -1 ) , as these are exactly the conditions that we assumed when analyzing the range of DSP (recall that DSP ∈ ( -1 / 2 , 1 / 2 ) approximately).”

In a bi-colored half-split cycle with 5000 vertices, all measures yield positive scores for both partitioning scenarios (equal-sized and 90%-10%).

“We observe that all measures yield positive scores for both partitioning scenarios”

In a bi-colored alternating cycle with 5000 vertices, RWC and ARWC display a positive bias.

“As in the clique experiment, RWC and ARWC display a positive bias.”

For real-world networks, DSP distinguishes ideologically polarized communities from structurally similar but neutralized configurations.

“Second, for real-world networks, DSP distinguishes ideologically polarized communities from structurally similar but neutralized configurations, further demonstrating its robustness to group size imbalances and addressing limitations of both RWC and traditional metrics.”

A lower value of alpha for phi_v (a RWR that restarts more often) leads to a lower value of z.

“A lower value of 𝛼 for 𝜙 𝑣 (a RWR that restarts more often) leads to a lower value of 𝑧 .”

In a bi-colored half-split barbell network with 2000 vertices, most measures correctly reach the desired polarization value of 1 in the balanced case.

“Most measures correctly reach this value in the balanced case”

In a bi-colored half-split cycle with 5000 vertices, DSP consistently achieves the highest possible score, along with a few other measures.

“DSP consistently achieves the highest possible score, along with a few other measures.”

Under the assumptions that for every v in R, sum_{w in R} pi_w(v)=1, and for every v in B, sum_{w in B} pi_w(v)=1, DSP is maximized.

“assume that for every 𝑣 ∈ 𝑅 it is 𝑤 ∈ 𝑅 𝜋 𝑤 ( 𝑣 ) = 1 , and for every 𝑣 ∈ 𝐵 it is 𝑤 ∈ 𝐵 𝜋 𝑤 ( 𝑣 ) = 1 . It is easy to see that these assumptions maximize the value of DSP to be”

• AssumptionThe authors state this as an assumption: For every vertex v in R, the sum of diffusion scores from vertices in R to v equals 1.
• AssumptionThe authors state this as an assumption: For every vertex v in B, the sum of diffusion scores from vertices in B to v equals 1.

In a bi-colored clique with 5000 vertices, RWC and ARWC exhibit a positive bias.

“We observe that RWC and its adaptive variant ARWC exhibit a positive bias.”

The value z1, which is a function of n and alpha, increases as alpha decreases.

“The value 𝑧 1 , which is a function of 𝑛 and 𝛼 , increases as 𝛼 decrease.”

Excluding influencers from the restart set corrects the bias for random graphs.

“As shown in Figure 1, a simple fix is to exclude influencers from the restart set, which corrects the bias for random graphs.”

In a bi-colored alternating cycle with 5000 vertices, denoising often worsens the results: measures that initially yield negative values become less negative or even turn positive after applying the proposed correction.

“We observe that the denoising often worsens the results: measures that initially yield negative values become less negative-or even turn positive-after applying the proposed correction.”

In a bi-colored half-split cycle with 5000 vertices, in several cases, the denoising approach reduces these values, worsening their performance.

“however, in several cases, the denoising approach reduces these values, hence worsening their performance.”

The range of DSP is from -1/2 * (n-2)/(n-1) to 1/2 * n/(n-1).

“The range of DSP is (-1 2 𝑛 -2 𝑛 -1 , 1 2 𝑛 𝑛 -1 ) .”

• AssumptionThe authors state this as an assumption: For every vertex v in R, the sum of diffusion scores from vertices in R to v equals 1.
• AssumptionThe authors state this as an assumption: For every vertex v in B, the sum of diffusion scores from vertices in B to v equals 1.

DSP produces a zero score for a fully connected clique regardless of the community sizes.

“such as producing a zero score for a fully connected clique regardless of the community sizes, as shown in Section 4.”

• AssumptionThe authors state this as an assumption: The function phi_v is arbitrary provided it does not depend on the colors of the vertices.

In a color-alternating cycle, there is a positive z = z(n,alpha) in (0,1) such that for every vertex v in V, h_c(v)(v)=z and h_c(v)(v)=1-z.

“The high level of symmetry in such a network implies that there is a positive 𝑧 = 𝑧 ( 𝑛, 𝛼 ) ∈ ( 0 , 1 ) such that, for every vertex 𝑣 ∈ 𝑉 , it holds that ℎ c ( 𝑣 ) ( 𝑣 ) = 𝑧 and ℎ c ( v ) ( 𝑣 ) = 1 -𝑧 .”

On G(n,p,l) networks, DSP exhibits near-zero scores as theoretically guaranteed.

“On 𝐺 ( 𝑛, 𝑝, ℓ ) networks, DSP exhibits near-zero scores as theoretically guaranteed.”

DSP correctly captures the expected polarization of reference topologies such as monochromatic-splittable networks.

“We show that DSP satisfies these desiderata, being near-zero for non-polarized structures such as cliques and random networks, while correctly capturing the expected polarization of reference topologies such as monochromatic-splittable networks.”

• AssumptionThe authors state this as an assumption: Monochromatic-splittable networks have a known expected polarization.

DSP is robust to group size imbalances.

“Second, for real-world networks, DSP distinguishes ideologically polarized communities from structurally similar but neutralized configurations, further demonstrating its robustness to group size imbalances and addressing limitations of both RWC and traditional metrics.”

When the two connected components of a monochromatic-splittable network are of the same size (|R|=|B|=n/2) and isomorphic, symmetry implies that there are non-negative values z1 and z2 such that [formula].

“In these cases, symmetry implies that there are non-negative values 𝑧 1 = 𝑧 1 ( 𝑛, 𝛼 ) and 𝑧 2 = 𝑧 2 ( 𝑛, 𝛼 ) such that”

In such symmetric monochromatic-splittable networks, z2 can be expressed as n/2 - z1.

“Thus, we can express 𝑧 2 as 𝑛 / 2 -𝑧 1 .”

In a bi-colored half-split barbell network with 2000 vertices, performance tends to degrade, particularly after denoising, in the unbalanced setting.

“but performance tends to degrade-particularly after denoising-in the unbalanced setting.”

DSP applied to U.S. Congress datasets uncovers trends of increasing polarization in recent years.

“Our method applied to U.S. Congress datasets uncovers trends of increasing polarization in recent years.”

Retaining at least 40% of the vertices reduces variability in the approximation across samples.

“To reduce variability in the approximation across samples, we should retain at least 40% of the vertices.”

For salloum, DSP classification performance remains stable across α values (AUC 0.68 using α=0.85 and 0.64 using α=0.35).

“Although the polarization scores are slightly lower for larger values of 𝛼 , the classification performance of DSP remains stable (0 . 68 using 𝛼 = 0 . 85 and 0 . 64 using 𝛼 = 0 . 35).”

Assortative mixing is correlated with polarization.

“Assortative mixing is known to influence network topology, and our experimental evaluation showed that it is also correlated with polarization (see Figure 8 and Figure 13).”

RWC and ARWC exhibit a positive bias on the G(n,p,l) null model.

“Consistent with previous observations, RWC and ARWC exhibit a positive bias, as do EI, BCC, CCA, and DM.”

DSP is sensitive to the choice of α: as α decreases, the DSP score also decreases.

“We observe that DSP is sensitive to the choice of 𝛼 : as 𝛼 decreases, the DSP score also decreases.”

Among the other measures, only AEI consistently produces near-zero values across all conditions on the G(n,p,l) null model.

“Among the other measures, only AEI consistently produces the desired near-zero values across all conditions.”

Color assortativity is not zero on a bichromatic clique with equal numbers of nodes of the two colors; it takes a slightly negative value.

“For example, it is not zero on a bichromatic clique, even in the case when there are equal numbers of nodes of the two colors, rather it takes a slightly negative value.”

Across all scenarios, only two measures consistently align with the expected behavior: DSP and AEI.

“Across all scenarios, only two measures consistently align with the expected behavior: DSP and AEI.”

ROC curves and corresponding AUC values are roughly the same across sample sizes for approximate DSP.

“Finally, the chart on the right shows that the ROC curves and the corresponding AUC values are roughly the same across sample sizes, indicating that even when using a small vertex set, the score has the same capability of distinguishing between polarized and non-polarized networks.”

DSP yields average scores close to 0 with minimal deviations across all tested average degrees and partition skews in G(n,p,l) random networks (n=10000, 1000 networks).

“The average DSP score is close to 0 with minimal deviations for all average degrees and partition skews, proving the robustness of the measure to the partition size and network density.”

BP shows a negative bias on the G(n,p,l) null model.

“In contrast, BP shows a negative bias.”

Retaining at least 20% of the vertices is needed to achieve a good approximation of the original DSP score.

“Figure 9 (top) shows that we need to retain at least 20% of the vertices to achieve a good approximation of the original score.”

DSP remains below 0.16 across all sessions on the bill-cosponsorship networks.

“Similarly, our findings on the bill-cosponsorship networks align with previous studies [18], as we also observe low polarization levels (DSP remains below 0.16 across all sessions).”

EI, BCC, CCA, and DM exhibit a positive bias on the G(n,p,l) null model.

“Consistent with previous observations, RWC and ARWC exhibit a positive bias, as do EI, BCC, CCA, and DM.”

Networks with higher polarization levels tend to show a stronger influence from color assortativity, as the Polaris baseline is closer to the observed value as polarization increases.

“Overall, networks with higher polarization levels tend to show a stronger influence from color assortativity, as the Polaris baseline is closer to the observed value as polarization increases.”

Sampling-based approximation reduces complexity to O(smk).

“This reduces the complexity to O( 𝑠𝑚𝑘 ) .”

For the bi-colored half-split cycle with 5000 vertices, the adjusted score ARWC NoInfl collapses to 0, even though the expected value for this highly polarized topology is close to 1.

“In particular, for the bi-colored half-split cycle with 5000 vertices (Figure 12), the adjusted score-ARWC NoInfl-collapses to 0, even though the expected value for this highly polarized topology is close to 1 (results for RWC No-Infl are similar).”

• AssumptionRests on an assumption: For the bi-colored half-split cycle with 5000 vertices, the expected polarization value is close to 1.

The improvement from excluding influencers does not generalize to more structured graph families.

“However, this improvement does not generalize to more structured graph families.”

Exact computation of DSP has total time complexity O(nmk).

“Thus, the exact computation of DSP has total time complexity O( 𝑛𝑚𝑘 ) .”

The influence of the degree distribution remains relatively constant across datasets, as indicated by the consistent gap between the CM baseline and the observed values.

“Meanwhile, the influence of the degree distribution remains relatively constant across datasets, as indicated by the consistent gap between the CM baseline and the observed values.”

Q yields an average score of 0 on the G(n,p,l) null model.

“As expected, Q yields an average score of 0, since it uses an Erdős-Rényi network as its null model.”

The biases of existing controversy measures occur because they conflate topological artifacts, such as low density, small network size, or uneven group splits, with genuine structural division.

“These biases occur because existing controversy measures conflate topological artifacts, such as low density, small network size, or uneven group splits, with genuine structural division.”

Many traditional methods, such as modularity or assortativity, rely on simplistic null models that often fail to capture the complex dynamics of real-world networks.

“Many traditional methods, such as modularity or assortativity, rely on simplistic null models that often fail to capture the complex dynamics of the real-world networks [16, 23].”

• cites [16] [16] Pedro Guerra, Wagner Meira Jr, Claire Cardie, and Robert Kleinberg. 2013. A measure of polarization on social media networks based on community boundaries. In ICWSM , Vol. 7. 215-224. -Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [23] [23] Philip Leifeld. 2018. Polarization in the social sciences: Assortative mixing in social science collaboration networks is resilient to interventions. Physica A: Statistical Mechanics and its Applications 507 (2018), 510-523. - sourceNot checked — no full text of the source

Smaller alpha values lead to more importance for the immediate neighbors of the starting vertex.

“The rationale is the same for the alternating cycle: smaller 𝛼 values lead to more importance for the immediate neighbors of the starting vertex, which, in this case, are vertices with the same color as the starting vertex.”

A color-alternating cycle is expected to exhibit negative polarization.

“A negative polarization is expected in this network, because each vertex is directly connected to only vertices of the other color, and thus it is more likely to access content (and interact with vertices) from the other color than its own.”

DSP treats each vertex as a potential source for a random walk, with all other vertices as targets.

“Instead, DSP treats each vertex as a potential source for a random walk, with all other vertices as targets.”

• Also stated in: § Abstract · p. 1 · plain

  “DSP removes the arbitrary concept of 'influencers' used by the popular Random Walk Controversy (RWC) score, instead treating every node as a potential origin for a random walk.”

A clique of n vertices, arbitrarily partitioned into R and B, possibly with |R| != |B|, should exhibit no structural polarization.

“A clique of 𝑛 vertices, arbitrarily partitioned into 𝑅 and 𝐵 , possibly with | 𝑅 | ≠ | 𝐵 | , should exhibit no structural polarization: every vertex is connected to every other vertex, so every vertex has the same opportunities of accessing content (or interacting with vertices) from its own partition as it does from the other partition.”

DSP avoids the bias from self-visiting by designing a probing process tailored to the task.

“We show how to avoid this bias by designing a probing process tailored to our task.”

By integrating a statistically principled null model into its core formulation, DSP advances polarization measurement beyond ad hoc corrections.

“By integrating a statistically principled null model into its core formulation, DSP advances polarization measurement beyond ad hoc corrections.”

Monochromatic-splittable networks, as long as at least one of |R| or |B| is much larger than the size of the cut, exhibit strongly positive polarization.

“As long as at least one of | 𝑅 | or | 𝐵 | is much larger than the size of the cut, these networks exhibit strongly positive polarization, because all but a few vertices of each color are connected only to vertices of the same color, and thus most interactions are between homochromatic vertices.”

DSP is statistically more principled than RWC, which incorporates products of probabilities with no clear statistical interpretation.

“As a result, DSP is statistically more principled than RWC, which incorporates products of probabilities with no clear statistical interpretation.”

DSP is designed to have an expected value of zero on G(n,p,l) networks, a labeled extension of Erdős-Rényi G(n,p) where edges and labels are assigned randomly, ensuring no structural correlation between the two.

“Unlike previous proposals, DSP is designed to have an expected value of zero on 𝐺 ( 𝑛, 𝑝, ℓ ) networks, a labeled extension of the Erdős-Rényi 𝐺 ( 𝑛, 𝑝 ) model where edges and labels are assigned randomly, thus ensuring no structural correlation exists between the two.”

As alpha goes to zero, the lower bound on the range of DSP is -1/2 * (n-2)/(n-1).

“As 𝑧 is a probability, it is bounded below by zero, thus allowing us to recover the lower bound on the range of DSP as -1 2 𝑛 -2 𝑛 -1 as 𝛼 goes to zero.”

RWC is sensitive to elementary network features such as size, density, and community balance, rather than capturing only genuine structural divisions.

“These results suggest RWC is sensitive to elementary network features such as size, density, and community balance, rather than capturing only genuine structural divisions.”

A bias in RWC is introduced when the walk's restart set overlaps with the target influencer set.

“However, a bias is introduced when the walk's restart set overlaps with the target influencer set.”

The probing process gives more weight to cross-community influence in unbalanced communities, where otherwise the smaller group could be drowned out.

“While this may seem counterintuitive, it serves to give more weight to cross-community influence in unbalanced communities, where otherwise, the smaller group could be drowned out.”

• AssumptionThe authors state this as an assumption: The function phi_v is arbitrary provided it does not depend on the colors of the vertices.

The reference networks (cliques, color-alternating cycles, monochromatic-splittable networks) have a simple enough structure to enable deriving the exact solution of the DSP polarization measure.

“These specific networks have a simple enough structure that enables deriving the exact solution of the DSP polarization measure.”

The maximum of DSP is attained when diffusions from a community only reach vertices within that same community.

“The maximum is attained when diffusions from a community only reach vertices within that same community, the hallmark of extreme structural polarization.”

In the original RWC formulation, the set of influencers was negligible compared to the network, so the bias was not apparent.

“In the original formulation, the set of influencers was negligible compared to the network (10 in networks with thousands of vertices), so the bias was not apparent.”

The minimum of DSP is attained when diffusions only reach vertices of the opposite community.

“The minimum is attained when diffusions only reach vertices of the opposite community.”

As z1 is upper bounded by n/2, the upper bound on the range of DSP is 1/2 * n/(n-1).

“As 𝑧 1 is upper bounded by 𝑛 2 , we recover the upper bound on the range of DSP as 1 2 𝑛 𝑛 -1 .”

The overlap between the restart set and the target influencer set artificially inflates the probability of a walk staying within its own community.

“This overlap artificially inflates the probability of a walk 'staying' within its own community, as a walk starting from an influencer has already reached its destination.”

RWC scores on real-world networks are often preserved after randomization with null models that preserve basic degree structure for d=0 and d=1.

“Its scores on real-world networks are often preserved even after randomization with null models that preserve basic degree structure (for 𝑑 = 0 and 𝑑 = 1 using the dk-series terminology [25]).”

• cites [25] [25] Priya Mahadevan, Dmitri Krioukov, Kevin Fall, and Amin Vahdat. 2006. Systematic topology analysis and generation using degree correlations. ACM SIGCOMM Computer Communication Review 36, 4 (Aug. 2006), 135-146. - sourceNot checked — no full text of the source

Negative values of DSP indicate that, on average, the network structure promotes cross-community diffusion more than within-community diffusion.

“A key advantage of DSP is that negative values are clearly interpretable: they indicate that, on average, the network structure promotes cross-community diffusion more than within-community diffusion.”

DSP can be interpreted as the average score of how likely a vertex is to receive information from a given community, where the average is taken over the distribution defined by the probing process.

“The resulting DSP measure can be interpreted as the average score of how likely a vertex is to receive information from a given community, where the average is taken over the distribution defined by our probing process.”

Color assortativity alone is insufficient to fully account for the observed polarization in less polarized networks, especially when the score is low.

“Nonetheless, the differences between the observed and Polaris values in less polarized networks suggest that color assortativity alone is insufficient to fully account for the observed polarization, especially when the score is low.”

DSP can reliably differentiate between polarized and non-polarized networks.

“The results of our experimental evaluation highlight how DSP can reliably differentiate between polarized and non-polarized networks.”

Even when using a small vertex set, DSP score has the same capability of distinguishing between polarized and non-polarized networks.

“Finally, the chart on the right shows that the ROC curves and the corresponding AUC values are roughly the same across sample sizes, indicating that even when using a small vertex set, the score has the same capability of distinguishing between polarized and non-polarized networks.”

DSP does not suffer from the biases exhibited by previous measures.

“It does not suffer from the biases exhibited by previous measures, as we show by analytically deriving DSP values on families of reference networks.”

In a study of collaboration networks, interventions targeting assortative mixing had little effect on the macroscopic polarization of the network.

“For example, in a study of collaboration networks, Leifeld [23] found that assortative mixing could indicate polarization, but interventions targeting it had little effect on the macroscopic polarization of the network.”

• cites [23] [23] Philip Leifeld. 2018. Polarization in the social sciences: Assortative mixing in social science collaboration networks is resilient to interventions. Physica A: Statistical Mechanics and its Applications 507 (2018), 510-523. - sourceNot checked — no full text of the source