**Network Glossary**

**Network**: In our context, an interbank network G is the pair (N, E) consisting of the set of nodes or vertexes N(G) = 1, …, n representing banks, and a set of edges E(G), or links, representing financial contracts among banks.**Edge**: If the network is directed, an edge is an ordered pair of nodes (i, j) representing in our context that bank i lends to banks j. A weight A_{ij}can be associated with the edge indicating, for instance, the nominal value of the contract. If the network is undirected the order of the pair is not relevant, (i, j) = (j, i) indicate the same edge.**Adjacency matrix:**The adjacency matrix A of size n * n where n is the order of the graph is defined as follows. The element A_{ij}is not zero if an edge goes from i to j. The component i, j of A_{ij}is the weight of the edge.**Bipartite**: A network is said to be bipartite if the nodes can be grouped in two classes such that no edge exists between any two node of the same class. In our context the network of banks and assets is a bipartite network.**Neighborhood**: The neighborhood of a node i is the set N_{i}= j ∈ N : (ij) ∈ E.**Out-degree**: The (connectivity) out-degree, or out-degree of a node i in G, denoted as k_{i}, is the number of edges outgoing from i. Similarly we can define the in-degree. If non specified we mean the total degree or the degree in the case edges are undirected.**Hub**: A vertex with large degree.**Path**: A path between two nodes i_{1}and i_{k}is a sequence of nodes (i_{1}, i_{2}, …, i_{k}) such that (i_{1}, i_{2}); (i_{2}i_{3}); (i_{k-1}; i_{k}) ∈ E. In other words it is a set of edges that goes from i_{1}to i_{k}.**Distance**: The distance between two vertexes is the number of edges in a shortest path connecting them.**Diameter**: The diameter is the maximum value of distance among all the possible pairs of nodes in the network.**Cycle**: A cycle is a closed path, that is in which the first and last vertices coincide.**Tree**: A tree is a subgraph of G without cycles. If it encompasses all the nodes (but not all the edges) is called spanning tree.**Root**: The root is the only vertex with no incoming edges.**Leaf**: A leaf is a vertex of degree one that is not the root.**Connected component**: A connected component in G is a maximal set of firms such that there exists a path between any two of them. We will say that two components are disconnected if there is no path between them. A connected graph is a graph consisting of only one connected component.**Centrality**: There are several measures of centrality that captures in different ways the importance of a node or of an edge. For instance, the betweenness centrality of an node capture the number of paths that has to go through node i in order to connect all the pairs of nodes in the network. The feedback centrality is in itself a class of centrality measures that capture the importance of a node in a recursive way, based on a linear combination of the importance of the nodes in its neighborhood.**Eigenvector**centrality belongs to this class and it is the solution, if it is exists unique and positive, of the eigenvalue equation associated with the adjacency matrix, Ax = λx.**Clustering coefficient**: The clustering coefficient measures the fraction of neighbours of node, averaged across the set of nodes, that are also neighbours. In other words, it measures the number of triangles that are realized in the network, relatively to the total number of possible triangles that could exist in the network.**Community**: A community is an intentionally underspecified notion indicating a group of nodes that are more densely connected among each other than with the nodes that are not in the group.**Motifs**: All the possible graphs of a given ‘little’ (e.g. 3, 4, 5 order). Their statistics contributes to characterize the topological properties of the network.

**Climate-Finance Glossary**

**EU- ETS:**European Emission Trading System. The EU ETS works on the ‘cap and trade’ principle. A ‘cap’, or limit, is set on the total amount of certain greenhouse gases that can be emitted by all plants and installations, regulated in the system. Within the cap, companies receive emission allowances, which they can trade with one another as needed. They can also buy limited amounts of international credits from emission-saving projects around the world[1]. It is considered the key tool for reducing industrial greenhouse gas emissions and covers around 45% of total emissions. For further information see: http://ec.europa.eu/clima/policies/ets/index_en.htm**Carbon Tax:**A carbon tax is an instrument for the internalization of environmental costs caused by the production and use of fossil fuels. Within the EU it could be introduced as an alternative system to the EU-ETS or as an additional tool for the sectors currently not covered under the EU-ETS system (such as transport, buildings, agriculture).**Energy Efficiency target:**a quantitative EU-wide goal for decreasing EU primary energy consumption. The target for 2020 was set at 20% energy savings compared to the projected use of energy in 2020. For more information, see: http://ec.europa.eu/energy/en/topics/energy-efficiency**Renewable Energy target:**a quantitative goal for the share of renewable energy. The target set for 2020 was 20% of final energy consumption should come from renewable energy sources. For more information, see: https://ec.europa.eu/energy/en/topics/renewable-energy**Carbon leakage**: Carbon leakage is the term often used to describe the risk of industrial production being shifted to other countries with lower or no constraints on greenhouse gas emissions. Since this would reduce the GHG emissions within the EU, but would increase emissions elsewhere. The sectors and sub-sectors which are deemed to be exposed to a significant risk of carbon leakage are those that figure in an official list which is valid for five years. For more information, see: http://ec.europa.eu/clima/policies/ets/cap/leakage/index_en.htm**Internal Energy Market/ Energy Union:**is the goal to establish a single competitive market for energy in Europe, improving the choice consumer’s choices and market access for suppliers. This requires considerable investments into the energy network. For more information, see: http://ec.europa.eu/priorities/energy-union/index_en.htm or http://europa.eu/legislation_summaries/energy/internal_energy_market/index_en.htm