Detailed Instructions: In this task, you will be presented with a context from an academic paper and a question separated with a
. You have to answer the question based on the context.
Problem:We used a set of global network indicators which allow us to encode each network layer by a tuple of features. Then we simply concatenated tuples as to represent each multi-layer network with a single feature vector. We used the following global network properties:

Number of Strongly Connected Components (SCC): a Strongly Connected Component of a directed graph is a maximal (sub)graph where for each pair of vertices $u,v$ there is a path in each direction ($u
ightarrow v$, $v
ightarrow u$).

Size of the Largest Strongly Connected Component (LSCC): the number of nodes in the largest strongly connected component of a given graph.

Number of Weakly Connected Components (WCC): a Weakly Connected Component of a directed graph is a maximal (sub)graph where for each pair of vertices $(u, v)$ there is a path $u \leftrightarrow v$ ignoring edge directions.

Size of the Largest Weakly Connected Component (LWCC): the number of nodes in the largest weakly connected component of a given graph.

Diameter of the Largest Weakly Connected Component (DWCC): the largest distance (length of the shortest path) between two nodes in the (undirected version of) largest weakly connected component of a graph.

Average Clustering Coefficient (CC): the average of the local clustering coefficients of all nodes in a graph; the local clustering coefficient of a node quantifies how close its neighbours are to being a complete graph (or a clique). It is computed according to BIBREF28.

Main K-core Number (KC): a K-core BIBREF13 of a graph is a maximal sub-graph that contains nodes of internal degree $k$ or more; the main K-core number is the highest value of $k$ (in directed graphs the total degree is considered).

Density (d): the density for directed graphs is $d=
rac{|E|}{|V||V-1|}$, where $|E|$ is the number of edges and $|N|$ is the number of vertices in the graph; the density equals 0 for a graph without edges and 1 for a complete graph.

Structural virality of the largest weakly connected component (SV): this measure is defined in BIBREF14 as the average distance between all pairs of nodes in a cascade tree or, equivalently, as the average depth of nodes, averaged over all nodes in turn acting as a root; for $|V| > 1$ vertices, $SV=
rac{1}{|V||V-1|}\sum _i\sum _j d_{ij}$ where $d_{ij}$ denotes the length of the shortest path between nodes $i$ and $j$. This is equivalent to compute the Wiener's index BIBREF29 of the graph and multiply it by a factor $
rac{1}{|V||V-1|}$. In our case we computed it for the undirected equivalent graph of the largest weakly connected component, setting it to 0 whenever $V=1$.
Question: What are the global network features which quantify different aspects of the sharing process?
Solution:
Number of Strongly Connected Components (SCC) Size of the Largest Strongly Connected Component (LSCC) Number of Weakly Connected Components (WCC) Size of the Largest Weakly Connected Component (LWCC) Diameter of the Largest Weakly Connected Component (DWCC) Average Clustering Coefficient (CC) Main K-core Number (KC) Density (d)