Violence against women in Brazil remains a significant issue, even with existing laws like the Maria da Penha Law and the Femicide Law. This study presents a computational approach for conducting a descriptive spatio-temporal analysis of such violence against women, using Divinópolis (Brazil) as a case study and utilizing public data from the Department of Justice and Public Security of Minas Gerais. The Leiden algorithm was used to identify spatially coherent clusters, which helps avoid fragmented groupings that could compromise the analysis. Additionally, this study analyzed temporal variations in standard deviations based on factors such as education level, race/color, and case risk classifications through scatter plots. The results indicate that neighbourhoods with a high incidence of violence show consistently elevated deviations, suggesting that victims come from diverse social and demographic backgrounds. These neighbourhoods tend to be located in areas with higher crime rates and greater socioeconomic vulnerability. The proposed methodology can be used for ongoing monitoring, allowing for the rapid identification of changes in violence patterns and supporting evidence-based preventive public policies.
CEUR ISSN1613-0073
Violence against women remains a serious human rights violation across various societies,
including Brazil. Despite the implementation of laws like the Maria da Penha Law [
Research highlights factors contributing to violence against women, including structural
inequality, inefective protective measures, and insuficient institutional support [
Institutional inadequacies are also critical. Only 8.3% of Brazilian municipalities have
specialized Women’s Police Stations, limiting access to support from [
To address the issue, this study applies the Leiden algorithm, an unsupervised graph-based
optimization method, to analyze the spatial distribution of cases in a case study of Divinópolis,
a Brazilian city located in the state of Minas Gerais, which has one of the highest crime rates
related to violence against women. A case study can contribute as a framework for developing
strategies to identify and monitor violence against women in other contexts that integrate
temporal and spatial analyses with oficial crime data. Therefore, this work aims to fill this
gap by applying the findings to provide a complementary approach to identifying critical areas
based on electronic monitoring, as suggested [
Violence against women comprises a wide range of physical, psychological, sexual, and
patrimonial aggressions that occur in a continuum that can culminate in death by homicide, a fact
that has been termed femicide [
In Brazilian contexts, although violence and femicide are criminalized by law [
In this way, this study builds on geospatial and network-based approaches to map unequal
risks across neighbourhoods and to inform prevention strategies. Prior work has applied
machine learning approaches based on clustering and density techniques to identify patterns
of the geospatial descriptive datasets [
The results presented in the Table 1 key findings include a 14.71% decrease in female victims of violent crimes between 2022 and 2023, with completed robbery being the most common crime at 59.77%. In contrast, domestic violence victims increased by 9.40% during the same period. Domestic violence has risen, while overall violent crimes have decreased.
In addition to crimes against women by category, the analysis also ranks the top 15 municipalities in the state for the highest incidents of violence against women, as illustrated in Figure 1. Belo Horizonte has the highest absolute number of cases, followed by Juiz de Fora, Uberlândia, and Contagem.
Divinópolis, with a population of 231,091, has a femicide rate of 0.021636 per capita, placing it among the cities with the highest rates in the state. This rate is higher than Ipatinga’s (0.0131) and similar to those of Betim (0.02185) and Sete Lagoas (0.02198). Unlike the metropolitan area of Belo Horizonte, Divinópolis serves as a medium-sized urban setting, allowing for a better analysis of local patterns and causes of violence against women, while still reflecting the structural challenges of similarly sized municipalities.
Therefore, the municipality’s rate of about 0.002 femicides per inhabitant, similar to critical cases in other areas, highlights its potential to guide targeted public policies and prevention strategies. This study’s methodological approach can be applied to other medium and small municipalities, aiding in the creation of evidence-based strategies to combat femicide.
Then, Divinópolis displays distinct internal spatial patterns regarding femicide records, as shown in Figure 2.
This section outlines the steps for constructing and analyzing the network of violence against
women in Divinópolis, Minas Gerais, Brazil. The study serves as a framework for identifying and
monitoring violence against women in other contexts through temporal and spatial analyses
with oficial crime data. All technical information, including source code and datasets, is
available in a public repository. [
The methodology involved data collection and preprocessing, followed by network modeling based on spatial relationships among neighborhoods. The Leiden algorithm was used for community detection, and a sociodemographic assessment of the clusters was conducted. Notably, the data were descriptive, using aggregated information at the census tract and neighborhood levels instead of precise coordinates or detailed geospatial data. Figure 3 summarizes the workflow by outlining the methodological steps from the approach, detailed in the following sections.
The data for this study were sourced from the Department of Justice and Public Security of Minas
Gerais [
The dataset preprocessing was four steps: (i) Removal of irrelevant columns (e.g., internal codes); (ii) Standardization of text, including accent removal and uppercase conversion; (iii) Correction of city name inconsistencies for geospatial data accuracy; and (iv) Elimination of invalid records labeled ”NOT INFORMED” or ”INVALID.”
The oficial urban map of Divinópolis was the primary source for constructing the spatial graph
[
Violence cases against women were classified into three risk levels: Non-Fatal, Potentially Fatal, and High Risk of Fatality. This classification was based on severity factors as crime nature, method, and completion status. Each factor was weighted to determine the final risk category. Along with victim age, race/color, and education level, these criteria facilitated a descriptive analysis by neighborhood, revealing areas with higher concentrations of severe cases and increased vulnerability.
Age, race/colour, education, and case risk classification are analyzed because these variables
capture intersectional dimensions repeatedly linked to victimization and barriers to protection,
as suggested by [
To analyze the spatial distribution of violence cases against women in Divinópolis, a geographic network was created with neighbourhoods as nodes and geographic proximity as edges. The number of cases defined the nodes, allowing for the application of community detection algorithms to identify clustering patterns. Although initial algorithms like Girvan-Newman, Louvain, and Label Propagation had limitations, the Leiden algorithm was ultimately chosen for its stability and ability to create well-connected communities through node movement and refinement, enhancing cluster quality. 4.
After testing Girvan-Newman, Label Propagation, and Louvain, the Leiden approach was
selected because it guarantees well-connected communities and improved stability through
refinement and aggregation steps, reducing the fragmentation observed with Louvain in
heterogeneous, weighted networks, as suggested by [
After conducting the Leiden community detection, descriptive analyses were conducted to
characterize victim profiles by neighborhood, focusing on demographic patterns related to
violence. Considering the intersectionality of feminicide [
The proposed pipeline is designed for continuous operation by public entities. Each newly recorded case triggers an incremental update: (i) the neighbourhood graph is refreshed; (ii) the Leiden community detection is re-executed to reorganize communities if needed; and (iii) dispersion metrics (standard deviations) for victims’ education, race/colour, and case risk classification are recomputed and plotted. If statistically meaningful shifts are detected in these dispersion curves or community membership, an alert is raised to prompt review by decision-makers.
In practical terms, this enables near-real-time supervision of territorial dynamics: a steady rise in dispersion within a high-incidence cluster may signal profile diversification or changing modalities of violence, prompting rapid coordination of legal, social, and policing services in the most afected group. The dashboard can refresh at fixed intervals or be event-driven upon data insertion, ensuring that prioritization and resource allocation reflect the current state of the phenomenon.
This section presents the results obtained for descriptive spatial analysis of violence against women in Divinópolis, Minas Gerais, Brazil. First, territorial groupings generated by the Leiden algorithm are discussed, highlighting geographical patterns and neighbourhoods with the highest incidence of cases. Then, variations in victims’ sociodemographic characteristics—such as education, race/colour, and case risk classification—are analyzed, focusing on the dispersion of these factors in the most afected neighbourhoods, aiming to identify areas with greater diversity and complexity in victim profiles.
Thus, the Leiden algorithm mapped violence against women by detecting clusters of spatial units as neighborhoods with similar characteristics. Through iterative refinement and modularity optimization, the algorithm groups areas based on the density and similarity of indicators (e.g., education level, race/color, and case classification), efectively highlighting regions with higher concentrations of reported cases. Each cluster was assigned a distinct color, visually distinguishing zones with shared social and geographic patterns. One of the key advantages of this unsupervised method is its ability to reveal latent structures in the data without prior labeling or predefined categories, making it particularly suitable for exploratory spatial analysis in contexts where patterns are complex and emergent, such as gender-based violence
To identify spatial clusters of neighbourhoods with similar violence profiles, the Leiden algorithm was applied to the network built based on geographical proximity and the number of recorded cases. Among tested methods, Leiden showed superior performance in terms of internal cohesion, cluster stability, and visual clarity. In this dataset, the outcome was clearer, more contiguous clusters aligned with neighbourhood adjacency and case intensities, as demonstrated in Figure 5, a property that is crucial for territorial policy applications.
Figure 5 demonstrates that neighborhoods with similar case counts tend to cluster together, reflecting coherent spatial patterns. The red community groups’ neighborhoods, such as Esplanada, Porto Velho, São João de Deus, and Interlagos, all exhibit high incidence and physical proximity, suggesting common vulnerabilities. The yellow community includes neighborhoods such as Jardim Nova América, Afonso Pena, and Santa Clara, which also have similar occurrence profiles.
The Del Rey neighborhood, located in the vicinity of the Niterói neighborhood, exhibits a
high incidence of cases despite its small territorial area, indicating possible local vulnerabilities
linked to socioeconomic factors or inadequate infrastructure. This pattern is consistent with
the femicide in Table 2 by neighbourhood reported by the [
This spatial segmentation clarifies critical hotspots and suggests important diferences even among neighboring areas. The analysis underscores that violence against women, though present throughout the urban territory, exhibits concentration patterns in certain regions, justifying localized interventions.
To understand victim profiles across neighbourhoods in Divinópolis, three variables were analyzed: education level, race/colour, and case risk classification. Initially, mean-based graphs for each variable did not reveal significant patterns due to high data dispersion. Therefore, the analysis shifted to the use of standard deviation, which proved to be a more efective metric for capturing the heterogeneity of victim profiles within each neighbourhood
Figure 6a shows the relationship between total cases and the standard deviation of victims’ education levels. Neighborhoods with high violence incidence (over 100 cases) exhibit stabilized high standard deviations, indicating considerable diversity in educational levels among victims. Figure 6b illustrates Leiden algorithm-generated communities highlighting neighborhoods with 100 to 160 violence reports.
The graph in Figure 6a shows that neighborhoods with high violence incidence have a stabilized, relatively high standard deviation in educational levels, indicating significant diversity among victims. However, among neighborhoods with the highest number of cases (between 100 and 160 total), some communities, like 1, 3, 4, 2, and 5, exhibit a predominantly uniform educational pattern.
Figure 6b indicates how these neighborhoods cluster in the shaded area, suggesting similar educational diversity characteristics that may signify common local features. Figures 7a and 7b exhibit similar behavior concerning victims’ race/color and case risk classification. Standard deviations remain high in neighborhoods with greater violence incidence, highlighting significant racial diversity among victims. The consistency of this measure can serve as a monitoring reference, with abrupt changes potentially signaling shifts in victim profiles over time.
Overall, standard deviation analysis proved more informative than mean-based analysis, providing essential insights. Stability in internal variations within high-incidence neighborhoods can serve as a useful indicator for continuous monitoring systems, enabling tracking potential changes in victim profiles or violence types. (a) Relationship between number of cases and standard deviation of victims’ education by neighborhood.
(b) Graph of Leiden-detected communities highlighting neighborhoods with 100 to 160 violence reports. (a) Relationship between number of cases and standard deviation of victims’ race/color by neighborhood.
(b) Relationship between number of cases and standard deviation of case risk classifications by neighborhood.
Spatially cohesive high-incidence clusters with stable internal heterogeneity indicate that
prevention should combine territorial targeting (e.g., coordinated action in high-risk clusters)
with tailored services that address diverse victim profiles within the same area (legal aid, shelters,
income support, and safer mobility), as suggested by [
This study investigated violence against women in Divinópolis, Brazil, from a descriptive geographic and spatial perspective. It proposed a methodology based on complex networks to identify territorial patterns related to violence. By constructing a neighborhood network among districts and applying the Leiden algorithm, the study identified spatially cohesive communities with similar rates of violence, highlighting significant geographical clusters that can inform targeted public policies.
The analysis of variations in the standard deviation of victim characteristics, such as education level, race/colour, and case risk classification, indicated that neighborhoods with a higher number of incidents tend to have diverse victim profiles while exhibiting stable dispersion patterns. These findings support the hypothesis that violence against women is linked to structural and contextual factors, suggesting that its territorial distribution is not random.
Methodologically, the Leiden algorithm proved to be a powerful, unsupervised, graph-based tool capable of revealing latent spatial structures and forming well-connected clusters through modularity optimization and iterative refinement. The visualization of these clusters using color-coded communities provided valuable insights into areas of concentrated risk. However, the scope of this study was limited to the application of the algorithm in an exploratory, descriptive context, and the approach remains dependent on reporting practices. Cluster quality is sensitive to graph construction and parameterization, and a more comprehensive evaluation—considering metrics such as modularity gain, cluster stability, and sensitivity to parameter settings—is necessary to validate its efectiveness in spatial analyses of gender-based violence.
For future research, it is advisable to replicate this methodology in various cities to assess its transferability and examine the influence of educational institutions and supportive organizations in the region. Investigating the correlation between economic dependency and incidents of violence could provide further insight into structural drivers. Additionally, analysing neighborhoods with low incidence rates is crucial to determine whether the absence of reported cases reflects actual safety or results from underreporting.
The authors thank the Federal Center of Technology of Minas Gerais (CEFET-MG) for their support during this study, particularly the Research and Graduate Studies Director and the Department of Computing at the Divinópolis campus. We also acknowledge the State Judiciary of Minas Gerais, Brazil, for providing essential oficial data for our research.
During the preparation of this work, the authors used ChatGPT, Gemini, and Grammarly to assist with translation from Portuguese to English and to perform grammar correction. After using these tools, the authors carefully reviewed and edited the manuscript as necessary and take full responsibility for the content of this publication.