Redundancy and resilience. (a) Simple model of network with 3 nodes (1, 2, and 3). Nodes 1 and 2 interact to perform process A (blue), implementing a function, with inputs and outputs from and to other unrepresented nodes (little blue arrows). Node 3 is structurally connected with nodes 1 and 2 but is assumed to present little effective connectivity and thus not to interact much with nodes 1 and 2. Each node, which can be a region of the brain, can contain multiple intrinsic processing units (subregions or neurons), working together and capable of plasticity, that is, of modification of their effective connectivity via synaptic tuning. One can define a quantity of mutual information between any two nodes in the network (see text). If the effective connectivity of node 3 with nodes 1 and 2 increases, node 3 will relay information between nodes 1 and 2, and the chaining of and will contribute to : node 3 and its wires can become an indirect, parallel, alternate carrier of signal for nodes 1 and 2. This represents a form of redundancy. (b) Extended model from (a) with two additional nodes, 4 and 5, assumed to support a process B, irrelatively independent from process A, through their interactions. A quantity of mutual information can also be defined between nodes 4 and 5, and any other nodes in the network. In this case, node 3 is placed in a position of “hub”; that is, it is highly connected structurally with the other nodes of the network (“degree” = 4 versus 2 connections). If its effective connectivity with all its neighbors (i.e., directly connected nodes) is increased, it will start indirectly relaying signals not only among nodes of the same process (A or B), but also between nodes subserving the different processes (A and B). Without further filtering to separate and channel sources of signals, there is thus a risk of cross-talk and interferences between the processes A and B. If for functional reasons, the processing capacity of node 3 becomes shared by processes A and B, and plasticity within the node manages to reduce cross-talk between them, for example, by serializing the access, and to handle the source separation and channeling problem, there is nevertheless a risk of “access conflict” for the resource represented by node 3. (c) Theoretical matrix of structural connectivity (i.e., adjacency matrix) informing the existence of structural connections between each pair of nodes in a network. The analysis of such matrix can identify all direct and indirect, alternate structural pathways between any two nodes , and sort them according to their “hop” distance, that is, the number of intermediary nodes along the pathway connecting and (which is 0 when the connection is direct, 1 when it has one relay, 2 when 2, and so on). (d) Two types of functionally relevant redundancy: degeneracy and pluripotency (see text). Assuming that it is functional, node 3 in (b) can potentially represent a pluripotent resource for both processes A and B.