Dependence is defined as adapting to the availability of something, while addiction refers to the compulsive use of something regardless of harmful consequences (3). Choliz (14) defined four common factors of dependence and addiction as lack of control, abstinence, tolerance, abuse, and disruption with other activities. Meanwhile, Sansone and Sansone (15) noted that misuse, abuse, dependence, and addiction were still not distinguished. Some studies used “addiction” and “dependence” interchangeably in the same study without clearly distinguishing them (e.g., 16). Therefore, we use SPD in the present study with caution to describe that the reinforcement of smartphone use might lead to problematic symptoms. Given the high prevalence and negative daily life consequences of SPD, which were increasingly noticed by mental health professionals, and would be necessary to analyze the mechanisms underlying SPD. The compensatory internet use theory (CIUT; 17) and the interaction of person-influence-cognition-execution (I-PACE; 18) theoretical models provided a robust theoretical foundation for understanding the causes of SPD. People, according to the CIUT, engage in excessive technology overuse to mitigate negative emotions. For instance, individuals might increase SPD in response to distress and negative emotions associated with unexpected events in daily life, such as enforced seclusion. Meanwhile, the empirical discovery-based I-PACE model revealed individual dispositions (e.g., cognitive responses and emotions) likely contributed to vulnerabilities in the occurrence and maintenance of SPD (17, 18).

Rumination and anxiety may be risk factors for SPD (19–21). For example, policy-enforced mitigation strategies may increase social isolation and loneliness (22, 23), which would trigger rumination and anxiety, leading to the likelihood of psychiatric disorders (24, 25). That was because, on the one hand, rumination was a cognitive process involving repetitive reflections on negative experiences and feelings, related to psychopathology (26). It comprised repetition and passive attention on distressing symptoms and potential sources or outcomes from them (21, 27) with the inability to eliminate negative information from memory, which was considered as a deficit in control processes (28, 29). Therefore, growing research has focused on the relationship between rumination and cognitive control (e.g., SPD in daily life; 20, 30, 31). On the other side, rising uncertainty caused by COVID-19 could cause anxiety, and rumination was also a significant trigger of anxiety symptoms (25, 32), which would expose individuals to negative emotions fueled by a perceived threat, injustice, and self-loss (33, 34). Such individuals were susceptible to slipping into repetitive and negative thoughts about distress, strangling communication, and curbing dynamic behaviors (20, 21) in response to unfavorable events. It facilitated deeper processing of affective-related patterns and amplified emotional states (27, 32), aggravating symptoms of anxiety by worsening a “sense of uncontrollability focused on the possibility of future threat, danger, or other potentially negative events” (35). Smartphone users with higher degrees of anxiety showed more SPD (19). Finally, according to the I-PACE, habitual behavior development was the result of interactions among susceptibility variables (e.g., social isolation), cognitive responses to specific stimuli (e.g., rumination) and feelings (e.g., anxiety), and executive functions (e.g., decision or inhibitory control), in which associations contribute to the chronic behavior development (18). Meanwhile, the CIUT focused on the overuse of digital technology as a compensatory coping strategy. Existing studies reported that the CIUT and I-PACE models could be used to explain SPD (33, 36, 37), and recent research has explored the psychopathological constructs that underpin problematic smartphone use through the I-PACE (38).

Despite the substantial contributions provided by previous studies, a recent investigation revealed that an individual’s intolerance of uncertainty significantly predicted SPD, in this context, rumination and anxiety were identified as mediators (11). A nuanced approach to understanding the differences between rumination and anxiety to specific SPD symptoms is lacking. SPD might involve heterogeneous states of different symptoms (e.g., “inability to control craving,” “feeling anxious and lost,” “withdrawal/escape,” and “productivity loss”), with each differing relative weight (1, 39). Similarly, rumination and anxiety were multidimensional constructs (27, 40). These different ingredients might have various actions on the symptoms (11). Therefore, ignoring structural or symptom heterogeneity would be problematic, as it might prevent a more microscopic understanding of symptom interactions from a “small world” perspective (41, 42). Specifically, the appearance of one symptom is considered to increase the probability of the emergence of interrelated symptoms, in turn, which could lead to episodes of illness. It differed from the latent variable model, which supposed unobservable latent variables resulting in observable symptoms (41). For example, individuals with SPD show different association strengths with rumination (30) and anxiety (11, 32, 33), indirectly confirming this drawback. Research in psychopathology would probably benefit from “moving beyond disorder-level analysis to a more fine-grained symptom-level analysis” (38, 43). Networks analysis, a symptom-oriented graphical approach, conceptualizes psychopathology as complex systems with nodes that interact and strengthen with each other through underlying causal connections (i.e., edges). It has provided the ability to visualize complicated relationships across psychological structures at a subtler level (e.g., components and symptoms), which could contribute to researchers elucidating the mechanisms that underlie the symptoms’ associated components and developing more accurate and targeted interventions (41, 44).

To our knowledge, no studies have examined how individual components of rumination and anxiety lead to specific SPD symptoms. Furthermore, even fewer analyses have been conducted in the particular group of preservice teachers. Educational inequities were prevalent worldwide before the pandemic, and the Chinese school system was also highly unbalanced (8, 13, 45). Focusing on them in economically underdeveloped areas and SPD symptoms would be significant for educational development. Therefore, the present study used network analysis to develop a model of the component-symptom associations across rumination and anxiety on preservice teachers’ SPD symptoms. Specifically, we studied (1) the unique associations among rumination and anxiety components with SPD symptoms, (2) the influential nodes that maintain the network structure, and (3) the most influential nodes that bridge the rumination and anxiety clusters to SPD symptom clusters.

The participants in this study were a group of preservice teachers who were forced to isolate on college campuses due to epidemic control measures. They were drawn from six universities in West China, and 1,610 valid matching responses were retained for analysis.

In Table 1 , we present the demographic characteristics of the study’s participants, their average age was 21.11 years (s = 2.13); 827 (51.4%) were female, and 783 (48.6%) were male. Additionally, the participants’ birthplace consisted of urban (30.0%) and rural (69.9%) areas, while their academic backgrounds varied, with 45.1% majoring in Science and Engineering, 40.4% in Humanities and Social Sciences, and 14.5% in Arts and Sports. Furthermore, we included information regarding family and relationship factors, such as whether they were the only child (13.9%), and the educational background of their fathers and mothers. Lastly, their romantic relationship lengths were recorded, with 56.4% reporting no current romantic relationship, and the remaining participants were distributed across different relationship durations. For detailed demographic information, see Table 1 .

We surveyed Chinese preservice teachers using a demographic information form, ruminative response scale, generalized anxiety disorder scale, and mobile phone addiction index scale.

Data were collected in two ways. One was in the classroom utilizing paper questionnaires in June 2022, and the other was collected online through Wenjuanxing, a Chinese online survey platform from July to September, and both ways used the same questionnaire. This multi-sample design delivered credible and reproducible empirical evidence that extended the external validity of experimental findings and responded to the replication crisis in psychological science research (50, 51). During the data collection procedure, participants were told to participate voluntarily, and informed consent was obtained from all. Participants were asked whether there was a period when they were obliged not to leave their residence due to epidemic policies. If the answer were “no,” they would not be invited to complete the following questionnaire. Additionally, the data collection was mainly based on a self-reported method, thus during actual implementation, after consultation with the participants and counselors, both offline and online data collection were measured in the classroom before weekly class meetings for an objective and accurate data collection process to control the impact of the external context impact if possible. We distributed 600 paper questionnaires and returned 560, with a response rate of 93.3%; 1400 electronic questionnaires were distributed and received a response rate of 84.1% for 1,082 returns. After screening out incomplete and invalid questionnaires, 1610 samples were available for the following analysis.

We used SPSS 25.0 for descriptive statistics, correlation analysis, etc., and network analysis ran on R version 4.1.0. First, because items contained 4-point ordinal scales, the graphical least absolute shrinkage, and selection operator in the qgraph package build the network structure (42, 52). Due to the massive estimated parameters in the network (i.e., 34 nodes need to estimate 595 parameters: 34 threshold parameters and 34*33/2 = 561 pairwise correlation parameters), it might lead to some false positive edges. Therefore, all edges in the network were reduced by the graphical lasso (glasso; 52, 53) algorithm, and the minor edges were set precisely to zero, which maximized the fit and explained the covariances across nodes with the fewest possible edges. Further, the hyperparameter γ, controlling the weighing between false positive edges and removed true ones, was set to 0.5 (54), along with the extended Bayesian Information Criterion model selected to obtain a parsimoniously accurate structure. In the network, the nodes represent items, and the edges refer to the correlations, with green for the positive direction and red for the negative; its width indicates the strength of the correlations.

Second, node centrality indices (i.e., strength, betweenness, and closeness) were weighed. Node strength is calculated by summing all the weights of edges connected directly to it, with a higher-strength node sharing a stronger direct connection with many other nodes. As increasing evidence suggested that betweenness and closeness would not be reliable (53), we calculated the node’s expected influence besides the strength, which simultaneously considers the positive and negative edge, and gives sums of edge weights of nodes, showing a better way to identify influential nodes with negative edges (55). Furthermore, to identify critical nodes for cluster connectivity, we used the networktools package to computer the bridge expected influence based on edge weights from a given node to other clusters (56). Those nodes having a higher bridge expected impact are assumed to perform a more significant role in activating nodes from the opposite clusters. A rigorous method was used to determine the centrality and bridge nodes with a blind 85th percentile cutoff on the values of both node and bridge expected influence to avoid possible confirmation bias in the interpretation of centrality statistics.

Finally, we used the bootnet package bootstrapping method to evaluate the estimation accuracy and robustness of the network (53). On the one side, the accuracy estimation was performed by drawing bootstrap confidence intervals (CIs) from each edge weight. Higher CIs of overlapping edge weights indicate lower accuracy of the graphical depiction. On the other side, centrality index stability was estimated by bootstrap resampling of a subset of the total samples. Specifically, it shows how the centrality index changes as the proportion of the sample subset decreases (e.g., comparing the whole samples with only 30% of them). The more rapidly the centrality shifts with decreasing sample proportions, the less stable it is. The correlation stability coefficient shows the maximum acceptable degree of sample reduction, with good above 0.70, acceptable above 0.50, and minimum not less than 0.25 (53).

We examined the means and variability of all items (see Supplementary Table A ) and reported the correlation coefficients between variables’ dimensions (see Table 2 ), according to the recommendations of Fried (57), a higher score indicated a stronger propensity for the trait. Table 2 displays the correlation coefficients between the variables dimensions. Anxiety is moderately positively correlated with brooding (r = .333, p < 0.01) and strongly positively correlated with reflection (r = .815, p < 0.01), indicating that higher anxiety levels are associated with increased brooding and heightened reflection tendencies. Furthermore, anxiety is positively correlated with inability to control craving (r = .475, p < 0.01), feeling anxious and lost (r = .490, p < 0.01), withdrawal/escape (r = .360, p < 0.01), and productivity loss (r = .406, p < 0.01), revealing that elevated anxiety levels are associated with greater inability to control cravings, intensified feeling anxious and lost, a heightened inclination toward withdrawal/escape, and strengthen productivity loss. Moreover, brooding and reflection are both positively correlated with inability to control craving (brooding: r = .362, p < 0.01; reflection: r = .440, p < 0.01), feeling anxious and lost (brooding: r = .327, p < 0.01; reflection: r = .397, p < 0.01), withdrawal/escape (brooding: r = .343, p < 0.01; reflection: r = .386, p < 0.01), and productivity loss (brooding: r = .340, p < 0.01; reflection: r = .417, p < 0.01). These findings provide a concise overview of the associations between these variables, offering support for further focus on micro-level relationships in subsequent analyses.

The network structure shows that items of anxiety and rumination were mainly clustered with the compact connectivity, compared to items assessing SPD were more distant and less connected (see Figure 1 ). Within the network, 34 items were displayed, 252 (44.9%) of 561 possible edges (weights range from -.073 to.569), and more positive edges (n = 221) than negative ones (n = 31) were observed in general. Furthermore, among cluster edges, the strongest were R5 (“Write down what you are thinking and analyze it”) and SPD3 (“You have tried to hide from others how much time you spend on your mobile phone”; edge weight.092); R5 (“Write down what you are thinking and analyze it”) and SPD4 (“You have received mobile phone bills you could not afford to pay”; edge weight = .078). The strongest negative associations between cluster edges were A7 (“Feeling afraid as if something awful might happen”) and R6 (“Think about a recent situation, wishing it had gone better”; edge weight = -.073); followed by R5 (“Write down what you are thinking and analyze it”) and SPD12 (“If you don’t have a mobile phone, your friends would find it hard to get in touch with you”; edge weight = -.069). Meanwhile, the cluster of SPD symptoms was internally intensive, and all associations were majority positive (weights range from -.020 to.569).

The sample strength and expected influence values are shown in Figure 2A . Some items showed a higher strength, e.g., items A4 (“Trouble relaxing”; strength value = 1.171), R3 (“Think why do I always react this way”; strength value = 1.226), R8 (“Think why can’t I handle things better”; strength value = 1.175), SPD2 (“You have been told that you spend too much time on your mobile phone”), and SPD6 (“You have attempted to spend less time on your mobile phone but are unable to”; strength value = 1.189), which indicated these items were the more cored nodes. Meanwhile, items R2 (“Analyze recent events to try to understand why you are depressed”; expected influence value = 1.027), R3 (“Think why do I always react this way”; expected influence value = 1.137), R7 (“Think why do I have problems other people don’t have”; expected influence value = 0.905), and R8 (“Think why can’t I handle things better”; expected influence value = 1.084) showing a great expected influence, were recognized as the central nodes of the symptom network. Finally, five bridging nodes are R2 (“Analyze recent events to try to understand why you are depressed”; bridge expected influence =.663), R3 (“Think why do I always react this way”; bridge expected influence =.824), R7 (“Think why do I have problems other people don’t have”; bridge expected influence =.627), R8 (“Think why can’t I handle things better”; bridge expected influence =.740), and SPD16 (“You find yourself occupied on your mobile phone when you should be doing other things, and it causes a problem”; bridge expected influence =.627) that had the greatest bridge expected influence (Details see Figure 2B ).

The relatively narrow 95% CIs of the bootstrap indicate that the edges of the network structure would be judged accurately (see Supplementary Figure S1 ), and we performed bootstrap difference tests for edge weights, node strength, expected influence, and bridge expected influence separately (see Supplementary Figures S2 - S5 ). These methods were based on the recommendations of Epskamp et al (53). In addition, the correlation stability coefficients for both node strength and expected influence decreased smoothly in line with the reducing proportion of sampled cases, and both (strength value = .594 and expected influence value = .750) were greater than 0.50, with CIs above 0.25 (see Figure 3 for details; 53). It demonstrated that the centrality indices of both node strength and expected influence were sufficiently stable.