Data collection

Between 24 February 2018 and 7 March 2018, we have collected 966,483 messages (tweets) posted by 194,273 different users to the microblogging platform Twitter, containing at least one of the following keywords or hashtags: “elezioni”, “#elezioni”, “#elezioni2018”, “#elezioni4marzo”, “#ItalyElection2018”, “#voto”, “#4marzo”, “#M5S”, “#PD”, “#LeU”, “#LiberieUguali”, “#ForzaItalia”, “#FDI”, “#FI”, “#lega”, “#FratellidItalia”, “#MDP”.

Tweets have been collected using the streaming real-time provided by Twitter API platform, filtered by the above keywords. Twitter by default limits to 1% of the overall number of Tweets per second the fraction of tweets that can be retrieved from the streaming API. However, when the fraction of tweets concerning specific keywords is smaller than 1% of the global volume, Twitter does not apply limitations and the complete flow of information is collected. When this is not the case, Twitter provides messages of warning, reporting the cumulative number of missed tweets.

In the case of Italian elections, we received no warnings, therefore we have collected 100% of tweets containing the specified keywords.

We complied with the Twitter’s terms of service to collect the data.

Classification task

In this work the classification of users in our data set as “humans” or “bots” is based on features providing the best classification accuracy according to recent studies [11, 12]: 1) Statuses count; 2) Followers count; 3) Friends count; 4) Favourites count; 5) Listed count; 6) Default profile; 7) Geo enabled; 8) Profile use background image; 9) Protected; 10) Verified. The total number of features is ten (N_feats = 10).

Searching for better performance we tested different machine learning techniques on an independent dataset created ad-hoc (see Supplementary Information) from a collection of manually annotated datasets (see Table 1). Models are trained on the 80% of the data and validated over the remaining 20%. The subdivision between the two sets was carried respecting the balancing between bots and humans present at the level of the single original datasets, in this way we have all type of different bots both in training and validation. The models based on random forest and deep neural network provided us with the highest accuracy (>90%) and precision in identifying bots (>95%). We chose the deep neural network model because it also provided a more stable classification of certain users playing the role of broadcasters (see Supplementary Information).

Fiedler partitioning, modularity, segregation and infiltration

Fiedler partitioning is a widely used technique from spectral graph theory for solving the min-max cut problem, i.e. partitioning a network in two components of similar size but connected by links whose total weights are the smallest possible [24]. Fiedler partitioning is obtained by considering the eigenvalue problem: (1) for a connected network represented by the weighted adjacency matrix W, with w_ij equal to the weight of the link between nodes i and j, and by a matrix D having the strength of nodes on its main diagonal. The spectral partitioning is obtained by identifying nodes relative to positive and negative entries in the second eigenvector q₂ relative to the second eigenvalue λ₂. q₂ and λ₂ are also called Fiedler vector and Fiedler value, respectively.

We use modularity [25] for identifying the polarization of users in the social bulk in two groups, labelled here by c₁ and c₂: (2)

Here, A_ij is 0 is users i and j did not interact, otherwise it is equal to the number of their interactions; s_i indicates the total number of interactions involving the i-th user, i.e. its strength, while s is the total number of interactions in the network. Polarization values Φ_F close to 0 indicate no antagonism between opposing factions, while Φ_F close to 1 is relative to strongly opposing factions.

We use the generalization of modularity to more than two groups for establishing the fragmentation of users in antagonizing social groups. The mathematical definition is similar to Eq (2), except for the fact that we consider more possible partitioning into a number communities (c₁, c₂, …, c_M) larger than 2. The number M of existing communities is not known a priori and an optimization process must be employed to discover best partitioning of the system.

We measure social segregation by considering the average size of connected components weighted by the number of their links. Indicating with the set of connected components and with the set of n_i nodes connected by e_i edges in the i-th connected component, we define social segregation as: (3)

Σ ranges between 0 (a network with a single connected component) and 1 (a network of isolated nodes with no links).

We define infiltration of a given type of users in a given social group i as the fraction of users of that type in group i, namely: (4) where is the number of groups, s_i is the number of accounts of class s in the i-th group and u_i is the number of users in that group.

Bot identification

To identify automated agents in the data set, we developed a deep neural network model (see Methods and SI), which classified 13.4% of users as bots, a value compatible to estimations during other voting events [10, 11, 12]. We built the network of interactions between human users and bots, including different types of social actions such as Retweets (i.e. a user sharing another user’s message), Mentions (i.e. a user mentioning another use in a message) and Replies (i.e. a user starting a discussion with another user). While Mentions and Replies can have both negative and positive connotations, Retweets are traditionally considered as a form of social endorsement [26, 17]: Users tend to retweet and thus endorse content they agree with.

Human-bot interactions: Homophily and centrality

Fig 1 shows the volumes for messages (i.e., Tweets) and the considered social actions for both bots and humans. Fig 1(a)–1(d) indicates the overall fraction of messages exchanged between bots and humans (a), and the fractions stratified by social interactions (b-d). Arrows go from the source to the recipient of an interaction, for instance user A (source) replying to user B (recipient) would be indicated with an arrow A → B. Most of the social interactions are from humans to bots (46%); Humans tend to interact with bots in 56% of mentions, 41% of replies and 43% of retweets. Bots interact with humans roughly in 4% of the interactions, independently on interaction type. This indicates that bots play a passive role in the network but are rather highly targeted by humans. Fig 1(e) shows the number of social interactions over time. The circadian rhythm is evident, i.e. at night the volume of messages generated by humans drops down. Also bots display a similar circadian rhythm, in agreement with previous observations [10, 12]. In general, bots contribute to 6% of the total number of social interactions occurred during the voting event (March 4 2018). Fig 1(f) reports the geographic locations of both human and bot users in the social system. Although most of the users are located in Italy, there are significant fractions of human users also located in the United States and in Europe, indicating the worldwide relevance of the Italian voting. Similarly, bots’ locations are distributed worldwide and they are present in areas where no human users are geo-localized such as Morocco, Peru, Finland or Indonesia.

The analysis of observed social interactions (links) between users (nodes) before, during and after the voting day revealed bot homophily, i.e., automated agents tend to interact more with other bots rather than with humans compared to random expectation (see SI). Since interactions encode content spread [16], this result indicates that bots share messages mainly with each other and hence can resonate with the same content, be it news or spam. Furthermore, if we quantify the centrality of a user in terms of the probability of finding it by exploring the web of interactions at random, then we find that bots are almost twice as central as humans (see SI). The above findings indicate that bots play the role of sinks for information flow. In fact, 9 out of 10 hubs—i.e., highly interacting users—are bots and they are mainly news media and public profiles of politicians, which usually act as broadcasters and drive online information flow [17, 15]. The analysis of topic frequency and associations in bot-generated messages confirms this trend: Bots act as broadcasters by repeating the same political content of human users, boosting the spread of hashtags related to the electoral process (see SI).

Information cascades identify different classes of influencers

The observed social interactions build a complex network with a heterogeneous connectivity distribution. Such systems are well known for being susceptible to cascading events [27, 28] and, in the case of online social networks, the phenomenon might manifest as collective action and faster diffusion of specific information [29, 1, 2, 30]. In information cascades, a single piece of information is originated by a seed user, it is endorsed by other users in his/her neighborhood and consequently re-shared across the network [29]. Cascade size depends on a variety of factors [31], including—but not limited—to the structure of the network and the information content, making their prediction rather difficult [30].

Since metadata provided by Twitter does not allow to fully reconstruct an information cascade—because of missing intermediary retweets—we are only able to measure the cascade size by the overall number of endorsements, i.e. retweets, received by each post. Therefore, cascades are represented by star networks and, for brevity, in the following we will simply refer to them as “cascades”.

We have tracked 83,593 information cascades during Italian elections and, for each one, we have analyzed the underlying structure by measuring its size, i.e. the number of times an information has been re-shared. As expected for complex networks with highly heterogeneous connectivity [27], the distribution of observed cascade sizes is heavy-tailed and compatible with a power law characterized by a scaling exponent γ = −2.33±0.04, similarly to size distribution in percolation theory or avalanches in self-organized criticality [32]. Cascade size ranges between 2 and 4,313.

We show in Fig 2(a) a heat map of cascade size vs. the size of initiators’ social neighborhood (i.e., the number of followers). As expected, on average, larger the number of followers larger the cascade size, with very few exceptions. Fig 2(b) shows the same data, with explicit information about user classification. This figure shows a good separation between human and bot behavior. Deeper information cascades are generated mostly by humans with a high number of followers, with the remarkable exception of one, User01, who produced the largest cascade among humans and bots despite having less than 100 followers.

Recently, dynamical activity-connectivity maps based on network and temporal activity patterns—or their variation—have been used to identify influential individuals or broadcasters during online protest diffusion [15] and contagion dynamics of extremist propaganda [33]. For instance, Bastos and Mercea [34] used hashtag trends for showing the existence of “serial activists”, users with ordinary numbers of followers but very prolific in producing content about multiple political topics and bridging together disparate communities. Gonzalez et al. [15] related topological properties, such as the ratio between incoming (friends) and outgoing (followers) connections, to dynamical properties, such as the ratio of received and posted messages.

Here, we argue that it is also plausible to relate individuals’ social influence to the size of information cascades they generates with their content [35]. To this aim, we propose a more complex map relating a topological feature, i.e. the number of outgoing connections (followers), and a dynamical feature, i.e. information cascade growth rate, defined by the ratio between a cascade size and its duration over time. Baseline social behavior during a specific event, such as the Italian election in our case, is defined by the medians of the two observables, like shown in Fig 2(c). This map allows to easily identify four categories of individuals in the social dynamics: i) hidden influentials, generating information cascades rapidly spreading from a small number of followers; ii) influentials, generating information cascades rapidly spreading from a large number of followers; iii) broadcasters, generating information cascades slowly spreading from a large number of followers; iv) common users, generating information cascades slowly spreading from a small number of followers. Remarkably, the topological and dynamical behavior of humans and bots is very different: during Italian elections, bots are mostly broadcasters (mostly media) and influentials (mostly political leaders). Fig 2(c) (right) highlights a positive correlation between cascade rate and size: Cascades involving more users tend also to flow over the interactions web at faster rates. This positive trend is stronger for cascades of sizes larger than 10². The stronger correlation for larger cascades suggests that they differ qualitatively from smaller cascades: Larger cascades contain specific semantic content, in this case political-related topics, which accelerate spreading.

The social bulk of endorsements mirrors political antagonism

So far, our analysis characterized online human behavior in terms of human-bot interactions and information spreading. However, to quantify to which extent the observed online social activity reflects the real world a more sophisticated analysis is required. To this aim, we analyzed the static representation of the system, where interactions across time have been aggregated to a directed and weighted social network. We then identified the core of the observed social system by tracking the most relevant interactions among the most important actors. We identified relevant interactions by assuming that if two users share similar political ideologies, they can endorse and subsequently share (i.e. retweet) the content of each other. However, if only re-sharing was considered, the network would contain a lot of spurious connections due, for instance, to fortuitous endorsement rather than to a systematic intention.

We first filtered the network by considering only pair of users with at least one retweet, with either direction, because re-sharing content it is often a good proxy of social endorsement [26]. We then considered a more selective restriction, by requiring that at least another social action—i.e., either mention or reply—must be present in addition to a retweet. This restrictive selection allows one to filter out all spurious interactions among users with the advantage of not requiring any threshold with respect to the frequency of interactions themselves. The resulting network is what we call the social bulk, i.e. a network core of endorsement and exchange among users. By construction, information flows among users who share strong social relationships and are characterized by similar ideologies: In fact, when a retweet goes from one user to another one, both of them are endorsing the same content, thus making non-directionality a viable approach for representing the endorsement related to content sharing. Therefore, in the following, we can safely consider undirected interactions among users. Connections between users are weighted by the aggregated frequency of their social interactions. An illustration of how the social bulk is built is shown in Fig 3(a).

In the following, we introduce different measures to quantify different features of the social bulk, i.e. social polarization, fragmentation and segregation.

The concept of social polarization assumes the existence of two competing stances or opposing groups characterizing the mesoscale organization of the system [36]. In presence of two groups, they can be identified by calculating, for instance, the Fiedler partitioning [24, 12], which is related to the min-max cut problem for finding optimal flows in networks [24]. Fiedler partitioning (see Methods) separates the users of a connected graph into two classes such that the total number of inter-class connections is close to the optimal minimum. If interactions encode strong social relationships, as in the social bulk, then the Fiedler partitioning identifies two factions antagonizing each other by sharing the least endorsements possible.

We measure social polarization by computing the modularity [25] of the social bulk with respect to its Fiedler partitioning (see Methods). The larger the modularity Φ of the Fiedler partitioning, i.e. system polarization, the more antagonized are users into two opposing groups. For the largest connected component of the social bulk we calculate the polarization Φ_F = 0.452. The expected polarization of a null model—where social relationships are uniformly randomized while preserving the individual degrees and the distribution of strengths—is , significantly different from the observed network (p-value < 10⁻⁵). This result indicates that the heterogeneity of social interactions can not explain, alone, the observed level of polarization, which has rather to be attributed to other causes such as political parties or opposing political trends. Notice that the social bulk analyzed here displays a higher modularity than other well studied social networks such as the Zachary Karate Club (Φ_F = 0.371) and the dolphin’s social network (Φ_F = 0.401)(cf. [37]). Considering that especially the Zachary Karate Club considers social interactions among two different groups, led by two different leaders and hence already highly polarized, then the above comparison further highlights the polarization of social interactions on the social media platform.

However, during the Italian elections considered in this work more than two political parties were present, so that the notion of polarization has to be extended to account for the presence of several opposing groups. For complex networks, a widely adopted approach is to use modularity maximization for group identification [25, 38, 39, 40]. Identified communities of users are characterized by intra-group connectivity denser than inter-group one.

In the case of the social bulk we can interpret modularity as an estimation of system’s social fragmentation into more than two opposing groups. Here, we use the Louvain multilevel approach, known to be very efficient on large-scale networks [41]. In the whole social bulk we measure a fragmentation Φ_L = 0.812, indicating the presence of several factions in the bulk network that are in a stronger opposition when compared to the null model (, p-value < 10⁻⁵). The fact that Φ_L > Φ_F indicates that a more accurate description of the mesoscale organization of the social bulk is given when more than two groups are considered, in agreement with our hypothesis that results should reflect the real world socio-political scenario. To understand if this finding is robust or just an artefact due to how the social bulk is built, we have measured the social fragmentation of the original system during all phases of voting (see Fig 4). Once again, we observe that social fragmentation is stable across time and significantly larger than random expectation, confirming that results obtained from the social bulk are consistent.

However, neither polarization nor fragmentation can be used to quantify to which extent the system consists of isolated groups—the ones with no interactions with the rest of the system—which are effectively segregated in the network. Note that we are not referring to users in the periphery [42, 43] of the system, where information can slowly but flawlessly flow among all nodes in the network. Instead, we refer to groups unable to exchange information with the core of the system, i.e., to nodes belonging to disconnected components. We quantify social segregationΣ by considering the average number of connected components weighted by the number of their links (see Methods). If a social network consists of isolated nodes only, then Σ = 1, whereas Σ = 0 for systems with a single connected component. For a network consisting of M connected components of same size and density of interactions Σ = 1 − 1/M: The larger the number of components, the larger the social segregation. The segregation of the social bulk is Σ = 0.476, significantly stronger than random expectation 〈Σ^rand〉 = 0.172 (p-value < 10⁻⁵) based on a configuration model preserving the connectivity distribution. This indicates that strong interactions lead to more segregated components, with fewer bridges among connected components than expected from the heterogeneity of interactions only. Hence, the observed segregation represents additional evidence for the presence of antagonism in the considered social ecosystem.

Polarization, fragmentation and segregation analyses all constitute evidence that the social bulk displays densely connected groups in opposition with each other.

Groups in the social bulk highlight digital augmentation

Through the multilevel approach, we identified 8 main opposing communities (i.e. having more than 2% of the total nodes in the network), as reported in Table 2. The analysis of hubs in each group of the social bulk indicates that i) one group corresponds to a single augmented human and his/her bots; ii) five groups directly map the ecosystems of the main Italian political parties; iii) two groups encode news media universe, either traditional or online news organisations.

In this context, we provide an operative definition of augmented humans as human users having at least 50% of bot neighbours in the social bulk. Users with less than 3 bulk interactions are discarded. We systematically identified 1,010 user accounts (12.7% of humans in the social bulk) corresponding to augmented humans. The most central augmented human in terms of number of social interactions is User01 which interacts with 2,700 bots and 55 humans in the social bulk. We have anonymized the username for privacy purposes.

It is natural to wonder about how bots, humans and augmented humans are organized into communities within the social bulk. In fact, given the relevance of the voting event in the real world, our hypothesis is that communities should reflect real political movements and groups, to some extent.

First, we focused our attention on the augmented human’s group, consisting of more than 2,500 automated agents artificially interacting with the augmented human user. This peculiar activity leads to a star-like structure for the corresponding community, as shown in Fig 3c, network C8. This finding has triggered our attention, driving our efforts towards quantifying the infiltration of a specific class s of accounts in each group, by considering the corresponding fraction of users in a given group (see Methods). Table 2 reports the infiltration of augmented humans in the groups of the social bulk. Unsurprisingly, infiltration of bots is higher in the group representing the augmented human and his/her automatic entourage of interacting social bots. Furthermore, we find that groups relative to news media are richer in bots compared to groups representing political parties, which is compatible with our previous finding of bots being preferentially news media broadcaster in the observed data.

The infiltration of augmented humans is approximately uniformly distributed across all identified groups, with the remarkable exception of C8, the augmented human’s community. One would expect for the groups richer in bots to have also more augmented humans. Instead, bot and augmented human infiltration do not correlate with each other (Kendall Tau 0.07, p-value 0.8), indicating that augmented humans tend to interact selectively with the bots available in their groups rather than creating more. This trend is not valid for the group C8, where one human (User01) interacts almost exclusively with bots.

Testing the role of news media

In the analysis of the social bulk we identified two communities corresponding to news media accounts. In order to test for the influence of these information hubs on human-bot interactions, we performed a test in which we checked the robustness of our results when all users in the above two communities identifying news media accounts were not considered. The removal of news media accounts led to negligible fluctuations (around 0.02) in the fractions of human-bot interactions (cfr. Fig 1(a)) and in the total volume of tweets produced by bots (around 0.4%). These results indicate that a prominent amount of human-bot interactions does not involve news media accounts and it is not influenced by the presence of information hubs.

Augmented humans are hidden influencers

All the augmented humans identified in this study have, on average, less than 9,000 followers and 1,500 friends, indicating that a considerable amount of social influence was obtained by users that preferentially interacted with bots during the considered event. The analysis of information cascades revealed that almost 2 out 3 augmented humans played an important role in the flow of online content: 67% of this class of users were either influentials or hidden influentials or broadcasters. Hidden influentials, known to be efficient spreaders in viral phenomena [44], are mostly humans but augmented humans also falls in this category (e.g. User01).

Groups in the social bulk reflect electoral outcomes

In order to investigate the representativeness of online groups in terms of real-world events beyond the hub analysis, we focused on the structural features of groups, namely the interaction volume of a group (i.e. the number of strong social interactions among users in the group) and the group size (i.e. the number of users in a given group). In Table 3, we show that the outcome of Italian elections (i.e. the fraction of votes received by each political group) strongly correlates with the group volume (Spearman rank correlation coefficient ρ = 0.9, p-value = 0.039). This correlation is statistically significant within a 5% significance level and direct sampling of rankings was used in order to compute the p-value without relying on any assumption about the large-scale statistical properties of the data. The strong correlation found indicates that the volume of online interactions closely mirrors the election outcome for this case study, although further research is needed to generalize this result and confirm its predictive power.