## Abstract

Many works related to Twitter aim at characterizing its users in some way: role on the service (spammers, bots, organizations, etc.), nature of the user (socio-professional category, age, etc.), topics of interest, and others. However, for a given user classification problem, it is very difficult to select a set of appropriate features, because the many features described in the literature are very heterogeneous, with name overlaps and collisions, and numerous very close variants. In this article, we review a wide range of such features. In order to present a clear state-of-the-art description, we unify their names, definitions and relationships, and we propose a new, neutral, typology. We then illustrate the interest of our review by applying a selection of these features to the offline influence detection problem. This task consists in identifying users who are influential in real life, based on their Twitter account and related data. We show that most features deemed efficient to predict online influence, such as the numbers of retweets and followers, are not relevant to this problem. However, we propose several content-based approaches to label Twitter users as influencers or not. We also rank them according to a predicted influence level. Our proposals are evaluated over the CLEF RepLab 2014 dataset, and outmatch state-of-the-art methods.

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## Acknowledgments

This work is a revised and extended version of the article *Detecting Real-World Influence Through Twitter*, presented at the 2nd European Network Intelligence Conference (ENIC 2015) by the same authors (Cossu et al. 2015). It was partly funded by the French National Research Agency (ANR), through the project ImagiWeb ANR-2012-CORD-002-01.

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## Centrality measures

### Centrality measures

In their description, we note \(G=(V,E)\) the considered cooccurrence graph, where *V* and *E* are its sets of nodes and links, respectively.

The degree measure *d*(*u*) is quite straightforward: it is the number of links attached to a node *u*. So in our case, it can be interpreted as the number of words co-occurring with the word of interest. More formally, we note \(N(u)=\{v\in V:\{u,v\}\in E \}\) the neighborhood of node *u*, i.e., the set of nodes connected to *u* in *G*. The degree \(d(u)=|N(u)|\) of a node *u* is the cardinality of its neighborhood, i.e., its number of neighbors.

The Betweenness centrality \(C_b(u)\) measures how much a node *u* lies on the shortest paths connecting other nodes. It is a measure of accessibility Freeman et al. (1979):

where \(\sigma _{vw}\) is the total number of shortest paths from node *v* to node *w*, and \(\sigma _{vw}(u)\) is the number of shortest paths from *v* to *w* running through node *u*.

The closeness centrality \(C_c(u)\) quantifies how near a node *u* is to the rest of the network Bavelas (1950):

where *dist*(*u*, *v*) is the *geodesic distance* between nodes *u* and *v*, i.e., the length of the shortest path between these nodes.

The Eigenvector centrality \(C_e(u)\) measures the influence of a node *u* in the network based on the spectrum of its adjacency matrix. The Eigenvector centrality of each node is proportional to the sum of the centrality of its neighbors Bonacich (1987):

Here, \(\lambda\) is the largest Eigenvalue of the graph adjacency matrix.

The subgraph centrality \(C_s(u)\) is based on the number of closed walks containing a node *u* (Estrada and Rodriguez-Velazquez (2005). Closed walks are used here as proxies to represent subgraphs (both cyclic and acyclic) of a certain size. When computing the centrality, each walk is given a weight which gets exponentially smaller as a function of its length.

where *A* is the adjacency matrix of *G*, and therefore \(\left( A^\ell \right) _{uu}\) corresponds to the number of closed walks containing *u*.

The *Eccentricity*
*E*(*u*) of a node *u* is its furthest (geodesic) distance to any other node in the network Harary (1969):

The *Local Transitivity*
*T*(*u*) of a node *u* is obtained by dividing the number of links existing among its neighbors, by the maximal number of links that could exist if all of them were connected (Watts and Strogatz (1998):

where the denominator corresponds to the binomial coefficient \(\left( {\begin{array}{c}d(u)\\ 2\end{array}}\right)\). This measure ranges from 0 (no connected neighbors) to 1 (all neighbors are connected).

The *Embeddedness*
*e*(*u*) represents the proportion of neighbors of a node *u* belonging to its own community Lancichinetti et al. (2010). The community structure of a network corresponds to a partition of its node set, defined in such a way that a maximum of links are located *inside* the parts while a minimum of them lie *between* the parts. We note *c*(*u*) the community of node *u*, i.e., the parts that contains *u*. Based on this, we can define the *internal neighborhood* of a node *u* as the subset of its neighborhood located in its own community: \(N^{int}(u)=N(u) \cap c(u)\). Then, the *internal degree*
\(d^{int}(u)=|N^{int}(u)|\) is defined as the cardinality of the internal neighborhood, i.e., the number of neighbors the node *u* has in its own community. Finally, the embeddedness is the following ratio:

It ranges from 0 (no neighbors in the node community) to 1 (all neighbors in the node community).

The two last measures were proposed by Guimerà & Amaral Guimerà and Amaral (2005) to characterize the community role of nodes. For a node *u*, the *Within Module Degree*
*z*(*u*) is defined as the *z*-score of the internal degree, processed relatively to its community *c*(*u*):

where \(\mu\) and \(\sigma\) denote the mean and standard deviation of \(d_{int}\) over all nodes belonging to the community of *u*, respectively. This measure expresses how much a node is connected to other nodes in its community, relatively to this community. By comparison, the embeddedness is not normalized in function of the community, but of the node degree.

The participation coefficient is based on the notion of community degree, which is a generalization of the internal degree: \(d_{i}(u)=|N(u) \cap C_{i}|\). This degree \(d_{c}\) corresponds to the number of links a node *u* has with nodes belonging to community number *i*. The participation coefficient is defined as:

where *k* is the number of communities, i.e., the number of parts in the partition. *P* characterizes the distribution of the neighbors of a node over the community structure. More precisely, it measures the heterogeneity of this distribution: it gets close to 1 if all the neighbors are uniformly distributed among all the communities, and to 0 if they are all gathered in the same community.

Both community role measures are defined independently from the method used for community detection (provided it identifies mutually exclusive communities). In this work, we applied the InfoMap method (Rosvall and Bergstrom (2008), which was deemed very efficient in previous studies (Orman et al. (2012).

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Cossu, JV., Labatut, V. & Dugué, N. A review of features for the discrimination of twitter users: application to the prediction of offline influence.
*Soc. Netw. Anal. Min.* **6, **25 (2016). https://doi.org/10.1007/s13278-016-0329-x

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### Keywords

- Influence
- Natural language processing
- Social network analysis